To determine To calculate: The solution of the system of equations, 4 r − 3 s = 8 and 2 r + 5 s = 8 by addition method. Explanation Given Information: The system of equations are 4 r − 3 s = 8 and 2 r + 5 s = 8 . Formula used: Addition method to solve a linear system of equations: Step 1. Write the equations in the form of a x + b y = c . Step 2. Multiply one or both equations by a constant, so that after adding the equations, there will be only one variable. Step 3. Add both the equations which will result in equation of one variable. Step 4. Compute the equation obtained in Step 3 and find the value of one variable. Step 5. Substitute the value obtained in Step 4 of one variable in any of the original equation to obtain other one. Step 6. Write the value of variables in correct order. Step 7. Check the solution by putting the calculated value in all equations in the system. Calculation: Consider the system of equations: 4 r − 3 s = 8 …… ( 1 ) 2 r + 5 s = 8 …… ( 2 ) Use equation ( 1 ) and equation ( 2 ) to eliminate r and solve for s : Multiply equation ( 2 ) by − 2 and add with equation ( 1 ) as; 4 r − 3 s = 8 − 4 r − 10 s = − 16 _ − 13 s = − 8 s = 8 13 Thus, the value of s is 8 13 . To determine r , substitute s = 8 13 in equation ( 1 ) as; 4 r − 3 s = 8 4 r − 3 ( 8 13 ) = 8 4 r = 128 13 r = 32 13 Thus, the value of r is 32 13

Intermediate Algebra For College Students (10th Edition)

10th Edition

ISBN: 9780134758992

Author: Allen R. Angel, Dennis Runde

Publisher: PEARSON

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Chapter 4, Problem 17RE

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To calculate: The solution of the system of equations, 4r−3s=8 and 2r+5s=8 by addition method.

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Chapter 4, Problem 16RE

Chapter 4, Problem 18RE

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