Explanation Given Information: The provided equations are x + 2 y − z = 0 , 3 x + y − 2 z = − 1 and x − 4 y + z = − 2 . Formula used: Follow the steps as mentioned below to solve the three equations by elimination method. Step1: Use any two equations to remove one variable by adding or subtracting. Step2: Use different pair of equations to remove the same variable that was removed in step1. Step3: Now solve the resultant equations obtained from step1 and step2. Step4: Put the values of variables obtained in step3 into any of three equations to get the value of third variable. Step5. Check the values computed by substituting them in the provided equations. Calculation: Consider the equations, x + 2 y − z = 0 …… (1) 3 x + y − 2 z = − 1 …… (2) And x − 4 y + z = − 2 …… (3) Now, eliminate the variable z by multiplying equation ( 1 ) by 2 and then subtract the equation ( 2 ) . 2 x + 4 y − 2 z = 0 − 3 x − y + 2 z = 1 − x + 3 y = 1 ¯ Now, take negative sign on both the sides. − ( − x + 3 y ) = − 1 x − 3 y = − 1 Then, x − 3 y = − 1 …… (4) Now, add equation ( 1 ) and ( 3 ) . x + 2 y − z = 0 x − 4 y + z = − 2 2 x − 2 y = − 2 ¯ Then, 2 x − 2 y = − 2 …… (5) Now, multiply equation ( 4 ) by − 2 and then add to equation ( 5 ) . − 2 x + 6 y = 2 2 x − 2 y = − 2 _ 4 y = 0 Then, y = 0 Put the value of y = 0 in equation ( 4 )

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ISBN: 9780321924711

Author: Marvin L. Bittinger

Publisher: PEARSON

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Chapter 4, Problem 14CR

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To calculate: The solution set of the equations x+2y−z=0, 3x+y−2z=−1 and x−4y+z=−2.

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Chapter 4, Problem 13CR

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The solution set of the equations x + 2 y − z = 0 , 3 x + y − 2 z = − 1 and x − 4 y + z = − 2 .

Solution Summary: The author explains how to solve the three equations by elimination method.

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To calculate: The solution set of the equations x+2y−z=0, 3x+y−2z=−1 and x−4y+z=−2.

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