Solve for x, y, z
x=-8
y=3
z=2
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3y-z=7 2x-3y+2z=-21 3x+y=-21
Reorder the equations.
z=3y-7
Solve 3y-z=7 for z.
2x-3y+2\left(3y-7\right)=-21
Substitute 3y-7 for z in the equation 2x-3y+2z=-21.
y=-\frac{2}{3}x-\frac{7}{3} x=-\frac{1}{3}y-7
Solve the second equation for y and the third equation for x.
x=-\frac{1}{3}\left(-\frac{2}{3}x-\frac{7}{3}\right)-7
Substitute -\frac{2}{3}x-\frac{7}{3} for y in the equation x=-\frac{1}{3}y-7.
x=-8
Solve x=-\frac{1}{3}\left(-\frac{2}{3}x-\frac{7}{3}\right)-7 for x.
y=-\frac{2}{3}\left(-8\right)-\frac{7}{3}
Substitute -8 for x in the equation y=-\frac{2}{3}x-\frac{7}{3}.
y=3
Calculate y from y=-\frac{2}{3}\left(-8\right)-\frac{7}{3}.
z=3\times 3-7
Substitute 3 for y in the equation z=3y-7.
z=2
Calculate z from z=3\times 3-7.
x=-8 y=3 z=2
The system is now solved.
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