Add 4z to the first equation to get an expression that will substitute for x.

x =

2(

-y + 2z = 2 (subtract 2, collect terms) [eqn 4]

2(

3y + 6z = 6 (subtract 2, collect terms) [eqn 5]

We can solve [eqn 5] for y and substitute the result into [eqn 4].

y + 2z = 2 (divide [eqn 5] by 3)

y =

-(

4z = 4 (add 2, collect terms)

Put this value of z into [eqn 6] to find y

y = 2 - 2(1)

Likewise, use the value of z in our expression for x

x = 1 + 4(1)

The complete solution is

x =

**1 + 4z**Use this in the other two equations.2(

**1+4z**) - y - 6z = 4 (substitute into the second equation)-y + 2z = 2 (subtract 2, collect terms) [eqn 4]

2(

**1+4z**) + 3y - 2z = 8 (substitute into the third equation)3y + 6z = 6 (subtract 2, collect terms) [eqn 5]

We can solve [eqn 5] for y and substitute the result into [eqn 4].

y + 2z = 2 (divide [eqn 5] by 3)

y =

**2 - 2z**(subtract 2z) [eqn 6]-(

**2 - 2z**) + 2z = 2 (substitute for y in [eqn 4])4z = 4 (add 2, collect terms)

**z = 1**(divide by 4)Put this value of z into [eqn 6] to find y

y = 2 - 2(1)

**y = 0**Likewise, use the value of z in our expression for x

x = 1 + 4(1)

**x = 5**The complete solution is

**x=5, y=0, z=1**.