Solve for x, y, z
x=-3
y=8
z=4
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2x+5y-z=30 3x-3y+4z=-17 -2x+2y-6z=-2
Reorder the equations.
z=2x+5y-30
Solve 2x+5y-z=30 for z.
3x-3y+4\left(2x+5y-30\right)=-17 -2x+2y-6\left(2x+5y-30\right)=-2
Substitute 2x+5y-30 for z in the second and third equation.
y=-\frac{11}{17}x+\frac{103}{17} x=13-2y
Solve these equations for y and x respectively.
x=13-2\left(-\frac{11}{17}x+\frac{103}{17}\right)
Substitute -\frac{11}{17}x+\frac{103}{17} for y in the equation x=13-2y.
x=-3
Solve x=13-2\left(-\frac{11}{17}x+\frac{103}{17}\right) for x.
y=-\frac{11}{17}\left(-3\right)+\frac{103}{17}
Substitute -3 for x in the equation y=-\frac{11}{17}x+\frac{103}{17}.
y=8
Calculate y from y=-\frac{11}{17}\left(-3\right)+\frac{103}{17}.
z=2\left(-3\right)+5\times 8-30
Substitute 8 for y and -3 for x in the equation z=2x+5y-30.
z=4
Calculate z from z=2\left(-3\right)+5\times 8-30.
x=-3 y=8 z=4
The system is now solved.
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