# How do you solve 2x+2y-4z=8, 2x+y-z=6, -x-y+2z=2?

Dec 15, 2017

This system of equations has no solution.

#### Explanation:

Given:

$\left\{\begin{matrix}2 x + 2 y - 4 z = 8 \\ 2 x + y - z = 6 \\ - x - y + 2 z = 2\end{matrix}\right.$

Note that adding twice the third equation to the first we get:

$0 = 12$

which is false.

So this system is inconsistent and has no solutions.