Solve for x, y, z
x=1
y=-2
z=5
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x=-2y+z-8
Solve x+2y-z=-8 for x.
2\left(-2y+z-8\right)+3z=17 -3\left(-2y+z-8\right)-y+2z=9
Substitute -2y+z-8 for x in the second and third equation.
y=-\frac{33}{4}+\frac{5}{4}z z=15+5y
Solve these equations for y and z respectively.
z=15+5\left(-\frac{33}{4}+\frac{5}{4}z\right)
Substitute -\frac{33}{4}+\frac{5}{4}z for y in the equation z=15+5y.
z=5
Solve z=15+5\left(-\frac{33}{4}+\frac{5}{4}z\right) for z.
y=-\frac{33}{4}+\frac{5}{4}\times 5
Substitute 5 for z in the equation y=-\frac{33}{4}+\frac{5}{4}z.
y=-2
Calculate y from y=-\frac{33}{4}+\frac{5}{4}\times 5.
x=-2\left(-2\right)+5-8
Substitute -2 for y and 5 for z in the equation x=-2y+z-8.
x=1
Calculate x from x=-2\left(-2\right)+5-8.
x=1 y=-2 z=5
The system is now solved.
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