Explanation Given Information: The system of equations is 5 x + 7 = 8 y , 3 x = 8 y − 4 . Formula used: The elimination method is used to solve a system of equations and it allows the elimination of a variable. Step 1: Multiply the equations by a certain number first if needed. Step 2: Solve the equations for one variable by the addition principle. Step 3: Substitute the value of the variable obtained in step 2 in any of the provided equations to compute the value of the second variable. Calculation: Consider the system of equations, 5 x + 7 = 8 y , 3 x = 8 y − 4 Collect all the like terms on one side and label the equations as follows: 5 x − 8 y = − 7 …… ( 1 ) 3 x − 8 y = − 4 …… ( 2 ) Multiply the equation ( 2 ) by − 1 as follows: − 3 x + 8 y = 4 …… ( 3 ) Add equation ( 1 ) and ( 3 ) as follows: 5 x − 8 y = − 7 − 3 x + 8 y = 4 _ 2 x + 0 = − 3 Solve for x as follows: 2 x = − 3 x = − 3 2 Now substitute x = − 3 2 in equation ( 1 ) and solve for y as follows: 5 x − 8 y = − 7 5 ( − 3 2 ) − 8 y = − 7 − 15 2 − 8 y = − 7 − 8 y = 1 2 Solve further as follows: − 8 y = 1 2 y = 1 2 ⋅ − 1 8 = − 1 16 The solution of the provided system of equation is ( − 3 2 , − 1 16 )

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ISBN: 9781323235911

Author: BITTINGER

Publisher: Pearson Custom Publishing

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Chapter 14.6, Problem 27ES

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To calculate: The solution of the system of equations 5x+7=8y,3x=8y−4.

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Chapter 14.6, Problem 26ES

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Ch. 14.1 - Prob. 1SR Ch. 14.1 - Prob. 2SR Ch. 14.1 - Prob. 1DE Ch. 14.1 - Prob. 2DE Ch. 14.1 - Prob. 3DE Ch. 14.1 - Prob. 4DE Ch. 14.1 - Prob. 5DE Ch. 14.1 - Prob. 6DE Ch. 14.1 - Prob. 7DE Ch. 14.1 - Prob. 8DE

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The solution of the system of equations 5 x + 7 = 8 y , 3 x = 8 y − 4 .

Solution Summary: The author explains the elimination method used to solve a system of equations.

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To calculate: The solution of the system of equations 5x+7=8y,3x=8y−4.

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