Verified answer

-2x + 6y + 2z = 2

3x + y - 2z = - 2 _____ADD

x + 7y = 0

x + 7y = 0

2x + 5y = 3

-2x - 14y = 0

2x + 5y = 3____ADD

-9y = 3

y = - 1/3

2x - 5/3 = 3

2x = 14/3

x = 7/3

-7/3 - 1 + z = 1

z = 2 + 7/3

z = 13/3

x = 7/3 , y = -1/3 , z = 13/3

There are many ways to solve a system of equations. I would solve it by having my calculator invert the coefficient matrix: type in [[ -1 3 1][ 2 5 0 ][ 3 1 -2]]^(-1) * [[1][3][-2]].

Presumably you are studying a particular method and need to practice with that.

If you're learning the elimination method, the fact that one equation already lacks a z is a good place to start.

Add twice the first equation to the third.

Double the resulting equation and subtract the second original equation.