Solve for x, y, z
x=5
y=-2
z=1
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2x-2y-z=13 3x-5y+5z=30 x-2y=9
Reorder the equations.
z=2x-2y-13
Solve 2x-2y-z=13 for z.
3x-5y+5\left(2x-2y-13\right)=30
Substitute 2x-2y-13 for z in the equation 3x-5y+5z=30.
y=\frac{13}{15}x-\frac{19}{3} x=2y+9
Solve the second equation for y and the third equation for x.
x=2\left(\frac{13}{15}x-\frac{19}{3}\right)+9
Substitute \frac{13}{15}x-\frac{19}{3} for y in the equation x=2y+9.
x=5
Solve x=2\left(\frac{13}{15}x-\frac{19}{3}\right)+9 for x.
y=\frac{13}{15}\times 5-\frac{19}{3}
Substitute 5 for x in the equation y=\frac{13}{15}x-\frac{19}{3}.
y=-2
Calculate y from y=\frac{13}{15}\times 5-\frac{19}{3}.
z=2\times 5-2\left(-2\right)-13
Substitute -2 for y and 5 for x in the equation z=2x-2y-13.
z=1
Calculate z from z=2\times 5-2\left(-2\right)-13.
x=5 y=-2 z=1
The system is now solved.
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