Solve for x, y, z
x=-3
y=3
z=2
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y=6x+2z+17
Solve 6x-y+2z=-17 for y.
x+2\left(6x+2z+17\right)-z=1 2x+2\left(6x+2z+17\right)-3z=-6
Substitute 6x+2z+17 for y in the second and third equation.
x=-\frac{33}{13}-\frac{3}{13}z z=-40-14x
Solve these equations for x and z respectively.
z=-40-14\left(-\frac{33}{13}-\frac{3}{13}z\right)
Substitute -\frac{33}{13}-\frac{3}{13}z for x in the equation z=-40-14x.
z=2
Solve z=-40-14\left(-\frac{33}{13}-\frac{3}{13}z\right) for z.
x=-\frac{33}{13}-\frac{3}{13}\times 2
Substitute 2 for z in the equation x=-\frac{33}{13}-\frac{3}{13}z.
x=-3
Calculate x from x=-\frac{33}{13}-\frac{3}{13}\times 2.
y=6\left(-3\right)+2\times 2+17
Substitute -3 for x and 2 for z in the equation y=6x+2z+17.
y=3
Calculate y from y=6\left(-3\right)+2\times 2+17.
x=-3 y=3 z=2
The system is now solved.
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