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