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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.

Verified Answer :

I think its he didnt eliminate the same variables

frika

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

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