Q:

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 = −20A) 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

Accepted Solution

A:
Answer:Option D) multiply y by 4 in the first equation and subtract the second equationStep-by-step explanation:we have2x+y=-10 ----> first equation3x+4y=-20 ---> second equationVerify each casecase A) multiply the first equation by 4 and subtract the second equationso(2x+y)*4=-10*4 ------> 8x+4y=-40[8x+4y=-40]-[3x+4y=-20] -----> 5x=-20 -----> x=-4This step is correctcase B) multiply the first equation by -4 and add the second equationso(2x+y)*-4=-10*-4 ------> -8x-4y=40[-8x-4y=40]+[3x+4y=-20] ----->-5x=20 -----> x=-4This step is correctcase C)  add 8 times the first equation and −2 times the second equationso(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=-4This step is correctcase D) multiply y by 4 in the first equation and subtract the second equationso2x+4y=-10[2x+4y=-10]-[3x+4y=-20] -----> -x=-10+20 -----> x=-10This step is incorrectNOT produce a system with the same solution