Explanation Given Information: The provided system of equations is, 2 x + 3 y = 5 3 x + 2 y = 5 Formula used: Elimination Method: This method is used to find the solutions of the system of linear equations by eliminating one of the two variables from the equations. Multiply the equations with suitable non-zero numbers. Then combine the equations in such a way so that one of the variables get eliminated and then evaluate the value of the other variable. Then substitute the value of this variable in either of the equations to get the value of the first variable. Calculation: Consider the equations, 2 x + 3 y = 5 …… (1) 3 x + 2 y = 5 …… (2) Multiply equation (1) by 2 and equation (2) by − 3 . 2 ( 2 x + 3 y ) = 2 ( 5 ) 4 x + 6 y = 10 …… (3) − 3 ( 3 x + 2 y ) = 5 − 9 x − 6 y = − 15 …… (4) Add equations (3) and (4) to eliminate the variable y . 4 x + 6 y = 10 − 9 x − 6 y = − 15 _ 4 x − 9 x = 10 − 15 − 5 x = − 5 Then evaluate the value of the variable x . − 5 x = − 5 5 x = 5 x = 1 Substitute x = 1 in the equation 2 x + 3 y = 5 and evaluate the value of the variable y . 2 ( 1 ) + 3 y = 5 2 + 3 y = 5 3 y = 5 − 2 3 y = 3 Simplify it further, 3 y = 3 y = 1 So, ( x , y ) = ( 1 , 1 ) seems to be the solution of the provided system of equation. To find the solution of the system of equations, graphically, plot the graphs of the equations and find the intersection point. To plot the graph of the equations, find the ordered pairs. Consider the equation, 2 x + 3 y = 5 Substitute x = 0 in the equation 2 x + 3 y = 5 . 2 ( 0 ) + 3 y = 5 0 + 3 y = 5 3 y = 5 y = 5 3 Substitute x = 5 2 in the equation 2 x + 3 y = 5 . 2 ( 5 2 ) + 3 y = 5 5 + 3 y = 5 3 y = 0 y = 0 Substitute x = − 2 in the equation 2 x + 3 y = 5

Finite Mathematics and Application Calculus (Looseleaf) - Text Only

7th Edition

ISBN: 9781337291484

Author: Waner

Publisher: Cengage

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Chapter 4.1, Problem 12E

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To calculate: The solution to the system of equations 2x+3y=5 and 3x+2y=5 and check the answers graphically.

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Chapter 4.1, Problem 11E

Chapter 4.1, Problem 13E

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Finite Mathematics and Application Calculus (Looseleaf) - Text Only

Ch. 4.1 - In Exercises 1-6, find three different particular...Ch. 4.1 - In Exercises 1-6, find three different particular...Ch. 4.1 - In Exercises 1-6, find three different particular...Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E Ch. 4.1 - In Exercises 7-20, find all solutions of the given...Ch. 4.1 - In Exercises 7-20, find all solutions of the given...Ch. 4.1 - In Exercises 7-20, find all solutions of the given...Ch. 4.1 - In Exercises 7-20, find all solutions of the given...

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The solution to the system of equations 2 x + 3 y = 5 and 3 x + 2 y = 5 and check the answers graphically.

Solution Summary: The author calculates the solution to the system of equations by eliminating one of the two variables from the equation.

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Chapter 4 Solutions