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Linear equation examples

Linear equations are equations of the first order. These equations are defined for lines in the coordinate system. An equation for a straight line is called a linear equation. The general representation of the straight-line equation is y=mx+b, where m is the slope of the line and b is the y-intercept.. Linear equations are those equations that are of the first order More examples of linear equations Consider the following two examples: Example #1: I am thinking of a number. If I add 2 to that number, I will get 5. What is the number? Although it may be fairly easy to guess that the number is 3, you can model the situation above with a linear equation What is Linear Equation?. A linear equation is an algebraic equation in which the highest exponent of the variable is one. Linear equation has one, two or three variables but not every linear system with 03 equations. Usually, a system of linear equation has only a single solution but sometimes, it has no solution or infinite number of solutions.. A two variables linear equation describes a. Example: y = 2x + 1 is a linear equation: The graph of y = 2x+1 is a straight line . When x increases, y increases twice as fast, so we need 2x; When x is 0, y is already 1. So +1 is also needed; And so: y = 2x + 1; Here are some example values Solve the linear equation [tex]\frac{3}{8}a=3[/tex] . Problem 24. Solve the equation 4x - 9 = 2x + 7. Problem 25. If [tex]5x+12=3x-24[/tex], determine the value of x. Problem 26. Find the solution to the equation [tex]\frac{x}{5}=8[/tex].. Problem 27. If 28 = 10y - 3y, find y.. Problem 28-2х - 6 = 2.

One variable. Frequently the term linear equation refers implicitly to the case of just one variable.. In this case, the equation can be put in the form + =, and it has a unique solution = − in the general case where a ≠ 0.In this case, the name unknown is sensibly given to the variable x.. If a = 0, there are two cases.Either b equals also 0, and every number is a solution There can be many ways to solve linear equations! Let us see another example: Example: Solve these two equations: x + y = 6 −3x + y = 2; The two equations are shown on this graph: Our task is to find where the two lines cross. Well, we can see where they cross, so it is already solved graphically Examples of Linear Equations. The simplest linear equation is the one with one variable: ax + b = 0. A little bit of algebraic manipulation makes it clear that the unique solution to this linear equation is always -b/a. If the linear equation has two variables, they are usually called x and y. Then the equation can be written as . ax + by + c = To summarize how to write a linear equation using the slope-interception form you Identify the slope, m. This can be done by calculating the slope between two known points of the line using the slope formula The linear equation has only one variable usually and if any equation has two variables in it, then the equation is defined as a Linear equation in two variables. For example, 5x + 2 = 1 is Linear equation in one variable. But 5x + 2y = 1 is a Linear equation in two variables. Let us see some examples based on these concepts. Solved Examples

Linear Equations (Definition, Solutions, Formulas & Examples

  1. Real world linear equations in action as well as free worksheet that goes hand in hand with this page's real world ,word problems
  2. Linear Equation: A linear equation is an algebraic equation. In linear equation, each term is either a constant or the product of a constant and a single variable. If there are two variables, the graph of linear equation is a straight line. General form of the linear equation with two variables is given below:-y = mx + c, m ≠ 0
  3. Definition of Linear Equation of First Order. A differential equation of type \[y' + a\left( x \right)y = f\left( x \right),\] where \(a\left( x \right)\) and \(f\left( x \right)\) are continuous functions of \(x,\) is called a linear nonhomogeneous differential equation of first order.We consider two methods of solving linear differential equations of first order
  4. Equations reducible to linear form. Consider the following examples to see how we can reduce equations involving ratios into linear form. Now, simplify => 6x + 12 + 12x + 15 = 14x + 16 => 18x + 27 = 14x +16; Transpose the variable term 'x' to the left side and the numerical terms on the right side of the equation by changing their sign
  5. In this section we give a process for solving linear equations, including equations with rational expressions, and we illustrate the process with several examples. In addition, we discuss a subtlety involved in solving equations that students often overlook

Linear Equations - Definition and Examples

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Solving Linear Equations - So.. Linear equations like y = 2x + 7 are called linear because they make a straight line when we graph them. These tutorials introduce you to linear relationships, their graphs, and functions Linear Equations. Linear equations are those which make straight lines when graphed. Real life examples include: Calculating wages based on an hourly pay rate; Calculating medicine doses based on patients' weights; Calculating the perimeters of squares; Hiring a car if a deposit is paid and there is an hourly charge; Algebraic examples include.

Most people chose this as the best definition of linear-equation: An algebraic equation, su... See the dictionary meaning, pronunciation, and sentence examples Check the equation for varying terms and constant terms. Varying terms are numbers like , , or , where the number changes depending on what you plug into the variable, or letter.Constant terms are numbers like , or , where the number never changes.. Usually, equations won't come with varying terms and constant terms lined up on separate sides Graphing is one of the simplest ways to solve a system of linear equations. All you have to do is graph each equation as a line and find the point(s) where the lines intersect. For example, consider the following system of linear equations containing the variables x andy: y = x + 3 y = -1x - A linear differential equation of the first order is a differential equation that involves only the function y and its first derivative. Such equations are physically suitable for describing various linear phenomena in biology, economics, population dynamics, and physics. So let's begin Both equations are linear equations in standard form, with P(x) = -4/ x. Since . the integrating factor will be . for both equations. Multiplying through by μ = x −4 yields. Integrating each of these resulting equations gives the general solutions: Example 5: Sketch the integral curve of . which passes through the origin

Linear Equations (Types and Solved Examples) - ExamPlannin

Example 1: Consider the equation 7x - 35 = 0. On solving we have 7x = 35 or x = 5. The above linear equation is only true if x = 5 and hence the given linear equation has only one solution i.e. x = 5.. Example 2: Consider the equation 9(x - 1) - 35 = 8x + 37. On solving we have 9x - 9 - 35 = 8x + 37.. Collect the like terms on both sides by transferring them, we hav Worked examples: slope-intercept intro. Practice: Linear equations word problems. This is the currently selected item. Next lesson. Graphing slope-intercept equations. Linear equation word problems. Our mission is to provide a free, world-class education to anyone, anywhere. Khan Academy is a 501(c)(3) nonprofit organization There are simple problems that involve linear equations. For example, the sum of 35 and a number is 72. What is the number? The thing we don't know is our variable. Let's use x here Linear Algebra is a branch of mathematics that enables you to solve many linear equations at the same time. For example, if you had 15 lines (linear equations) and wanted to know if there was a. Moreover, a system of equations is a set of two or more equations that must be solved at the same time. For this reason, a system could also be called simultaneous equations. The word simultaneous means occurring at the same time I will only provide you with real life examples that lead to a system of linear equations and how to set up the.

Linear Equations - MAT

Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor Graphing Linear Equations: Examples. T-Charts Plotting & Drawing Examples More Examples. Purplemath. As long as you do your work neatly and orderly, you shouldn't have much trouble with graphing linear equations. Here are some more examples. Graph . First I'll do my T-chart Linear equations arise in a lot of practical situations. For example, consider the two widely used temperature scales: Celsius and Fahrenheit. To convert from the Fahrenheit scale to the Celsius scale, the following relation is used: \[F = \left( {\frac{9}{5}} \right)C + 32\] Note carefully that this is a linear equation in the two variables F.

Linear equations in one variable are equations where the variable has an exponent of 1, which is typically not shown (it is understood). An example would be something like \(12x = x - 5\). To solve linear equations, there is one main goal: isolate the variable.In this lesson, we will look at how this is done through several examples You can also test an equation is linear or nonlinear by plotting it on the graph. If an equation gives a straight line then that equation is a linear equation. Example: y = 2x + 1 is the equation can be represented on the graph as Here it represents a straight line so it is a linear equation

Graphing Linear Equations The graph of a linear equation in two variables is a line (that's why they call it linear ). If you know an equation is linear, you can graph it by finding any two solutions ( x 1 , y 1 ) and ( x 2 , y 2 ) Example 5: Solve the following equation: 12 + 2(3 x − 7) = 5 x − 4 . Use the four steps to solving a linear equation, as follows: 1a. Distribute and combine like terms. 1b. Place like terms adjacent to each other and simplify. 2a. Move variables to the left side of the equation. In this example, add −5 x to each side of the equation. 2b The solution is not ordinarily obtained by computing the inverse of 7, that is 7 -1 = 0.142857..., and then multiplying 7 -1 by 21. This would be more work and, if 7 -1 is represented to a finite number of digits, less accurate. Similar considerations apply to sets of linear equations with more than one unknown; MATLAB ® solves such equations without computing the inverse of the matrix Solve systems of linear equations in matrix or equation form. Solve System of Linear Equations. This section shows you how to solve a system of linear equations using the Symbolic Math Toolbox™

This report represents GCD, euclidean algorithm, linear diophan-tine equation and linear congruential equation. It investigates the methods for solving linear diophantine equations and linear congru-ential equations in several variables. There are many examples which illustrate the methods for solving equations. solving equations This sections illustrates the process of solving equations of various forms. It also shows you how to check your answer three different ways: algebraically, graphically, and using the concept of equivalence.The following table is a partial lists of typical equations Our study of linear algebra will begin with examining systems of linear equations. Such linear equations appear frequently in applied mathematics in modelling certain phenomena. For example in linear programming, profit is usually maximized subject to certain constraints related to labour, time availability etc.These constraints can be put in the form of a linear system of equations Examples of linear equation in a sentence, how to use it. 85 examples: The resulting linear equation was solved for using a banded solver. - Th

Simple/Linear Equation Problems: Problems with Solution

An equation such as y=x+7 is linear and there are an infinite number of ordered pairs of x and y that satisfy the equation. The slope, m, is here 1 and our b (y-intercept) is 7. The slope of a line passing through points (x1,y1) and (x2,y2) is given b Examples of solving linear ordinary differential equations using an integrating factor by Duane Q. Nykamp is licensed under a Creative Commons Attribution-Noncommercial-ShareAlike 4.0 License. For permissions beyond the scope of this license, please contact us Combinations of linear equations. Linear equations can be added together, multiplied or divided. A simple example of addition of linear equations. C(x) is a cost function. C(x) = fixed cost + variable cost. R(x) is a revenue function. R(x) = selling price (number of items sold) profit equals revenue less cost. P(x) is a profit function. P(x. In this video, we go over the definition of a linear equation. We begin with examples of linear equations about one variable, then those about two variables,.. Linear equation in one variable: An equation with linear expressions in one variable only is known as a linear equation in one variable. For example, $$5x+8 =9-x $$ Linear equation in two variables: An equation which can be put in the form ax +by +c =0, where a, b and c are real numbers and x,y are variables, is called a linear equation in two variable

Linear Equations - 4 Variables by: Staff Part I Question: by Katy Hadrava (Bemidji, MN) Solve the system of linear equations and check any solution algebraically. (If there is no solution, enter NO SOLUTION. If the system is dependent, set w = a and solve for x, y and z in terms of a. Do not use mixed numbers in your answer.) x + y + z + w = 1 LINEAR EQUATIONS - Solve for x in the following equation. Example 1: 5 x - 6 = 3 x - 8. Subtract 3x from both sides of the equation: Add 6 to both sides of the equation: Divide both sides by 2: The answer is x = - 1 Check the solution by substituting -1 in the original equation for x A Diophantine equation is a polynomial equation whose solutions are restricted to integers. These types of equations are named after the ancient Greek mathematician Diophantus. A linear Diophantine equation is a first-degree equation of this type. Diophantine equations are important when a problem requires a solution in whole amounts. The study of problems that require integer solutions is. For example, consider the following system of linear equations in two variables. [latex]\begin{align}2x+y&=15\\[1mm] 3x-y&=5\end{align}[/latex] The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently In the linear equation the value of coefficient is always equals to 0, which disturbs the pattern of the quadratic equation ax² and makes it the linear equation. Further a linear equation doesn't have any power higher than one of its own and it has the straight line form of ax+by+c=0 where the a,b,c are the respective constants

Matrix Random Input: octave:4> # octave:4> # Another Example using Random Function rand to Get Test Matrix: octave:4> C=rand(5,5) C = 0.0532493 0.4991650 0.0078347 0.5046233 0.0838328 0.0455471 0.2675484 0.9240972 0.1908562 0.0828382 0.2804574 0.9667465 0.0979988 0.8394614 0.4128971 0.1344571 0.9892287 0.9268662 0.4925555 0.1661428 0.0068033 0.2083562 0.1163075 0.7727603 0.3052436 octave:5. Word problems for systems of linear equations are troublesome for most of the students in understanding the situations and bringing the word problem into equations. We tried to explain the trick of solving word problems for equations with two variables with an example. Example: 2000 tickets were sold in an exhibition on Saturday Linear functions happen anytime you have a constant change rate. Pretty much any time your hear _____ per _____ or _____ for every _____ there is a linear equation involved as long as that rate stays constant. Linear equations all l.. Examples of Quadratic Equation A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared. The standard form is ax² + bx + c = 0 with a, b, and c being constants, or numerical coefficients, and x is an unknown variable

Linear equation - Wikipedi

Systems of Linear Equations - MAT

This equation relates the number of chirps per minute (y) made by a snowy tree cricket to the ambient temperature in degrees Fahrenheit (x). Figure 2: Three examples of linear relationships found in scientific applications. Early history of linear equations Linear Equations. A linear equation looks like any other equation. It is made up of two expressions set equal to each other. A linear equation is special because: It has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction Linear equation definition is - an equation of the first degree in any number of variables However, the word linear in linear equation means that all terms with variables are first degree. (The word linear in linear function means the graph is a line.) A linear equation can have 1, 2, 3, or more variables. So a linear equation is a linear function only if it has exactly 2 variables Solving Systems of Linear Equations by Graphing Examples. BACK; NEXT ; Example 1. Solve the following system of equations: The first equation is in standard form, which we can graph by finding the intercepts: The second equation is in point-slope form

Linear Function: Simple Definition, Example, Limit

Linear Equations - examples of problems with solutions for secondary schools and universitie Since, as we just wrote, every linear equation is a relationship of x and y values, we can create a table of values for any line. These are just the $$ x $$ and $$ y $$ values that are true for the given line. In other words, a table of values is simply some of the points that are on the line Solving Linear Equations by Elimination Method Examples : In this section, we will see some example problems using the concept elimination method. General form of linear equation in two variables is ax + by + c = Linear Equation in One Variable Linear Equation in One Variable. 1. Definition of an Equation: What is an equation? A statement of equality of two algebraic expressions in or more variables is called an equation. Examples: 1. x + 1 = 2 and 2. 2y + 3 =

Create printable worksheets for solving linear equations (pre-algebra or algebra 1), as PDF or html files. Customize the worksheets to include one-step, two-step, or multi-step equations, variable on both sides, parenthesis, and more Slope and Y-Intercept of a Linear Equation. For the linear equation y = a + bx, b = slope and a = y-intercept. From algebra recall that the slope is a number that describes the steepness of a line, and the y-intercept is the y coordinate of the point (0, a) where the line crosses the y-axis. Three possible graphs of y = a + bx

In [26, pages 33{35] there are examples of systems of linear equations which arise from simple electrical networks using Kirchho 's laws for elec-trical circuits. Solving a system consisting of a single linear equation is easy. However if we are dealing with two or more equations, it is desirable to have a systemati Linear equations are hard to learn and their reputation is well deserved. The reason for this is that linear equations are the first opportunity to practice operating with equations and develop equation solving skills. So if you are frustrated with linear equations, you are most likely not stupid and in a good company One example of a linear equation from real life is the equation which represents the physical phenomenon of air resistance in otherwise free fall. The equation -cv(t) = ma(t) is a linear equation. This may not be obvious to see, since a = [(d/dt)^..

Ex: Solve One Step Equations With Fraction by Multiplying

Writing linear equations using the slope-intercept form

Linear equations (equations whose graphs are a line) can be written in multiple formats, of a linear equation looks like this: Ax + By = C. A, B and C can be any number--including negative numbers, zero and one! So examples of standard form can look like this: 3_x_ + 7_y_ = 10, where A = 3, B = 7 and C = 10. Or they can look like. Linear equations mean the variable appears only once in each equation without being raised to a power. A system of linear equations means that all of the equations are true at the same time. So, the person solving the system of equations is looking for the values of each variable that will make all of the equations true at the same time An equation involves an unknown number, typically called x. Here is a simple example: x + 4 = 10. Some number, plus 4, equals 10. We say that an equation has two sides: the left side, x + 4, and the right side, 10. Because x appears to the first power, we call that a linear equation. A linear equation is also called an equation of the first.

Linear wave equation examples Acoustic (sound) wave. We will consider the acoustic or sound wave as a small amplitude disturbance of ambient conditions where second order effects can be ignored. We start with the Euler continuity and momentum equations \[\tag{9} \frac{\partial\rho}{\partial t}+\nabla\cdot\left(\rho v\right) = 0,\ A linear equation is defined as an equation where the greater power of the unknown is one. Examples. x+5=12 5x-3=44 x=9 In all the above examples the highest power of x is one Solving simple linear equations. To solve simple linear equations the following points should be noted; the sign of any term changes when it is moved from either side of. Systems of Linear Equations Beifang Chen 1 Systems of linear equations Linear systems A linear equation in variables x1;x2;:::;xn is an equation of the form a1x1 +a2x2 +¢¢¢+anxn = b; where a1;a2;:::;an and b are constant real or complex numbers. The constant ai is called the coe-cient of xi; and b is called the constant term of the equation. A system of linear equations (or linear system. Linear equations are the simplest kind of equations you come across in maths. You may be asked to solve a linear equation: find x if 2x+7=31,. or to draw the graph of a linear equation such as y =2x+1, which is a straight line, or to solve simultaneous linear equations:. find x and y, where x+2y+3=8 and x+y=3.. We all solve linear equations in our heads all the time without even noticing it

3. Graphical Solution of a System of Linear Equations . A `2 ×2` system of equations is a set of 2 equations in 2 unknowns which must be solved simultaneously (together) so that the solutions are true in both equations. We can solve such a system of equations graphically.That is, we draw the graph of the 2 lines and see where the lines intersect Systems of Linear Equations examples. Tons of well thought-out and explained examples created especially for students (Note that with non-linear equations, there will most likely be more than one intersection; an example of how to get more than one solution via the Graphing Calculator can be found in the Exponents and Radicals in Algebra section.) There are some examples of systems of inequality here in the Linear Inequalities section For full functionality of this site it is necessary to enable JavaScript. Here are the instructions how to enable JavaScript in your web browser

Writing Linear Equations Using Real Life Example - YouTube

Difference Between Linear and Nonlinear Equations BYJU'

Possible Duplicate: Solving a linear equation I need to programmatically solve a system of linear equations in C# AND VB Here's an example of the equations: 12.40 = a * 56.0 + b * 27.0 + tx.. 1.2. SAMPLE APPLICATION OF DIFFERENTIAL EQUATIONS 3 Sometimes in attempting to solve a de, we might perform an irreversible step. This might introduce extra solutions

Regression equations are frequently used by scientists, engineers, and other professionals to predict a result given an input. These equations have many applications and can be developed with relative ease. In this article I show you how easy it is to create a simple linear regression equation from a small set of data A simple linear regression fits a straight line through the set of n points. Learn here the definition, formula and calculation of simple linear regression. Check out this simple/linear regression tutorial and examples here to learn how to find regression equation and relationship between two variables. using the slope and y-intercept

Linear Equations in the Real World

Worked examples and 115 questions up to GCSE level. The method of solving linear equations is introduced with easy examples and extended to equations where the variable is on both sides and equations involving brackets LINEAR EQUATIONS. The method of addition. The method of substitution. Section 2: More examples. Cramer's Rule: The method of determinants. Section 3: Three equations in three unknowns. T HIS LESSON DEPENDS on Lesson 9: Linear equations. Example 1. Solve simultaneously for x and y

Types of Equations and Examples - ExamPlannin

Word Problem Exercises: Linear Equations: General Questions: Kim and Cyndi are starting a business tutoring students in math. They rent an office for $400 per month and charge $40 per hour per student. If they have 15 students each for one hour per week how much profit do they make together in a month For some, it's a chance to solve a real-world example, so there's a level of excitement and sense of wonder. For others, it's groaning, and frustration on where to even begin. Well, in this lesson we're going to make Solving Linear Equation Word Problems manageable with easy to follow tricks and steps A set of Linear equations are represented by the matrix equation: aMatrix xVector = bVector . The aMatrix and bVector are given, and the xVector is the solution. The first example set of equations given above can be rewritten as: 3 X + 4 Y + 5 Z = 0 1 X - 10 Y + 1 Z = 0 1 X + 0 Y + 1 Z = 42.5 . The matrix form of these equations is

Linear Differential Equations of First Orde

Linear Equation in Two Variables An equation that can be written in the standard form Ax + By = C where A, B and C are real numbers but A and B cannot both be zero. Learning Objective: Students should be able to illustrate linear equations in two variables. 4. Determine whether or not each equation is a linear equation in two variables A linear equation does not contain variables with exponents other than __. 1 denominator The graph of a linear equation is always a ____. line Linear Equations Not Linear Equations Linear Equations 18 Examples of solving linear ordinary differential equations using an integrating factor Exponential growth and decay: a differential equation Another differential equation: projectile motio Linear equations in one variable mc-TY-simplelinear-2009-1 In this unit we give examples of simple linear equations and show you how these can be solved. In any equation there is an unknown quantity, x say, that we are trying to find. In a linear equation this unknown quantity will appear only as a multiple of x, and not as a function of x.

Class 8 Linear Equations - basics, problems and solved

Homogeneous Matrix Equations. If we write a linear system as a matrix equation, letting A be the coefficient matrix, x the variable vector, and b the known vector of constants, then the equation Ax = b is said to be homogeneous if b is the zero vector. For example, the following matrix equation is homogeneou Simple linear equation (coin problems with solution) fractions solve for x ; glencoe mathematics algebra 2 solutions manual ; Describe one real-life example of where rational equations are used at home ; solving algebra equations with exponents ; motion algebra ; math solver ; real-life example of where rational equations are used at hom Enter your equation using Alt + = on the keyboard. Choose Convert and select professional to build your typed fractions to their Professional form into subscripts, or use Ctrl + =. You can similarly convert an equation back down to a linear format with Ctrl + Shift + =. Examples Equation 6.1.5 in the above list is a Quasi-linear equation. Homogeneous PDE : If all the terms of a PDE contains the dependent variable or its partial derivatives then such a PDE is called non-homogeneous partial differential equation or homogeneous otherwise Linear Equations In One Variable A statement of equality of two algebraic expressions, which involve one or more unknown quantities is known as an equation. A linear equation is an equation which involves linear polynomials. A value of the variable which makes the two sides of the equation equal is called the solution of the [

Algebra - Linear Equations

Solution: Transform the coefficient matrix to the row echelon form:. Since , we have to consider two unknowns as leading unknowns and to assign parametric values to the other unknowns.Setting x 2 = c 1 and x 3 = c 2 we obtain the following homogeneous linear system:. Therefore, and. Thus, the given system has the following general solution:. In view of the matrix properties, the general. Simultaneous equations and linear equations, after studying this section, you will be able to: solve simultaneous linear equations by substitution; solve simultaneous linear equations by elimination; solve simultaneous linear equations using straight line graphs; If an equation has two unknowns, such as 2y + x = 20, it cannot have unique solutions linear equations. In linear equation. A linear differential equation is of first degree with respect to the dependent variable (or variables) and its (or their) derivatives. As a simple example, note dy/dx + Py = Q, in which P and Q can be constants or may be functions of the independent Read More; measurement proble

Free linear equation calculator - solve linear equations step-by-step. This website uses cookies to ensure you get the best experience. By using this website, you agree to our Cookie Policy. Learn more Accept. Related » Graph » Number Line » Examples. This example shows you how to solve a system of linear equations in Excel. For example, we have the following system of linear equations Linear Equation vs Quadratic Equation. In mathematics, algebraic equations are equations which are formed using polynomials. When explicitly written the equations will be of the form P(x) = 0, where x is a vector of n unknown variables and P is a polynomial.For example, P(x,y) = x 4 + y 3 + x 2 y + 5=0 is an algebraic equation of two variables written explicitly Attempting to use a regression equation to predict values outside of this range is often inappropriate, and may yield incredible answers. This practice is known as extrapolation. Consider, for example, a linear model which relates weight gain to age for young children 6. Matrices and Linear Equations. by M. Bourne. We wish to solve the system of simultaneous linear equations using matrices: a 1 x + b 1 y = c 1 a 2 x + b 2 y = c 2. If we let `A=((a_1,b_1),(a_2,b_2))`, `\ X=((x),(y))\ ` and `\ C=((c_1),(c_2))` then `AX=C`. (We first saw this in Multiplication of Matrices). If we now multiply each side of . AX.

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