Solve for x, y, z
x=-2
y=3
z=2
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z=3x+2y+2
Solve 3x+2y-z=-2 for z.
-2x+y-3\left(3x+2y+2\right)=1 x-y+4\left(3x+2y+2\right)=3
Substitute 3x+2y+2 for z in the second and third equation.
y=-\frac{11}{5}x-\frac{7}{5} x=-\frac{7}{13}y-\frac{5}{13}
Solve these equations for y and x respectively.
x=-\frac{7}{13}\left(-\frac{11}{5}x-\frac{7}{5}\right)-\frac{5}{13}
Substitute -\frac{11}{5}x-\frac{7}{5} for y in the equation x=-\frac{7}{13}y-\frac{5}{13}.
x=-2
Solve x=-\frac{7}{13}\left(-\frac{11}{5}x-\frac{7}{5}\right)-\frac{5}{13} for x.
y=-\frac{11}{5}\left(-2\right)-\frac{7}{5}
Substitute -2 for x in the equation y=-\frac{11}{5}x-\frac{7}{5}.
y=3
Calculate y from y=-\frac{11}{5}\left(-2\right)-\frac{7}{5}.
z=3\left(-2\right)+2\times 3+2
Substitute 3 for y and -2 for x in the equation z=3x+2y+2.
z=2
Calculate z from z=3\left(-2\right)+2\times 3+2.
x=-2 y=3 z=2
The system is now solved.
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