Question

You are given the system of equations to solve by the elimination method, which is an INCORRECT step that will NOT produce a system with the same solution?

2x + y = −10
3x + 4y = −20

A) multiply the first equation by 4 and subtract the second equation
B) multiply the first equation by −4 and add the second equation
C) add 8 times the first equation and −2 times the second equation
D) multiply y by 4 in the first equation and subtract the second equation

Answer 1

Option D) multiply y by 4 in the first equation and subtract the second equation

Explanation:

we have

2x+y=-10 ----> first equation

3x+4y=-20 ---> second equation

Verify each case

case A) multiply the first equation by 4 and subtract the second equation

so

(2x+y)*4=-10*4 ------> 8x+4y=-40

[8x+4y=-40]-[3x+4y=-20] -----> 5x=-20 -----> x=-4

This step is correct

case B) multiply the first equation by -4 and add the second equation

so

(2x+y)*-4=-10*-4 ------> -8x-4y=40

[-8x-4y=40]+[3x+4y=-20] ----->-5x=20 -----> x=-4

This step is correct

case C) add 8 times the first equation and −2 times the second equation

so

(2x+y)*8=-10*8 ------> 16x+8y=-80

(3x+4y)*-2=-20*-2 ----> -6x-8y=40

[16x+8y=-80]+[-6x-8y=40] ----->10x=-40 -----> x=-4

This step is correct

case D) multiply y by 4 in the first equation and subtract the second equation

so

2x+4y=-10

[2x+4y=-10]-[3x+4y=-20] -----> -x=-10+20 -----> x=-10

This step is incorrect

NOT produce a system with the same solution