Question

Eliminate the “z” variable in the last two equations by finding opposite coefficients and adding. What is the resulting equation?

x + 3y + 2z = –16
2x – y + 2z = –15
2x – 2y – z = 1

Answer 1

answers
6x – 5y = –13
4x – 3y = –14
6x + 5y = 13
4x + y = –14

Answer 2

You can begin with any of two of the equations to eliminate z, but the problem says to use the last two equations, so let's do that. You want to add a multiple of equation #2, which has +2z term, and a multiple of equation #3, which has -z term. For example, 1 times eqn #2 plus 2 times eqn #3, gives +2z added to -2z, so the z terms cancel. You need to determine the rest of the sum. Probably can do it in your head, but if not, just write it out like an addition problem. Something like this...

1 times 2x – y + 2z = –15 becomes 2x - y + 2z = -15
2 times 2x – 2y – z = 1 becomes 4x - 4y - 2z = 2
adding those two equations (at the ends of the above two lines) gives
6x - 5y = -13