Question

Mark is solving the following system.

x+y+z=2 (1)
3x+2y+z=8 (2)
4x-y-7z=16 (3)

Step 1: He multiplies equation (1) by 7 and adds it to equation (3).
Step 2: He multiplies equation (3) by 2 and adds it to equation (2).

Which statement explains Mark’s mistake?
- He added equation (3) instead of equation (2) in step 1.
- He did not multiply equation (3) by the correct value.
- He did not eliminate the same variables in steps 1 and 2.
- He added equation (3) and equation (2) instead of subtracting.

Answer 1

I think its he didnt eliminate the same variables

Answer 2

Solving the system of linear equations Mark tries to apply elementary transformations in order to eliminate one variable.

He makes such steps:

1. He multiplies equation (1) x+y+z=2 by 7 and adds it to equation (3) 4x-y-7z=16. This gives him:

7x+7y+7x+4x-y-7z=14+16,

11x+6y=30.

2. He multiplies equation (3) 4x-y-7z=16 by 2 and adds it to equation (2) 3x+2y+z=8. This step gives him:

8x-2y-14z+3x+2y+z=32+8,

11x-13z=40.

Thus, he did not eliminate the same variables in steps 1 and 2.

Answer: correct choice is C