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 same number as equation (1).
He did not eliminate the same variables in steps 1 and 2.
He added equation the equations in step instead of subtracting them.

Answer 1

"He did not eliminate the same variables in steps 1 and 2."

Explanation: Step 1 (7·(1) + (3)) eliminates z and gives 11x + 6y = 30.
Step 2 (2·(3) + (2)) eliminates y and gives 11x − 13z = 40.

Those two new equations involve different pairs of variables (x,y) and (x,z), so you don't get a 2-variable system to solve. In elimination you must eliminate the same variable in both combinations.