Solve for x, y, z
x=1
y=-2
z=2
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z=2x 2x-3y+z=10 3x+2y+5z=9
Reorder the equations.
2x-3y+2x=10 3x+2y+5\times 2x=9
Substitute 2x for z in the second and third equation.
y=-\frac{10}{3}+\frac{4}{3}x x=-\frac{2}{13}y+\frac{9}{13}
Solve these equations for y and x respectively.
x=-\frac{2}{13}\left(-\frac{10}{3}+\frac{4}{3}x\right)+\frac{9}{13}
Substitute -\frac{10}{3}+\frac{4}{3}x for y in the equation x=-\frac{2}{13}y+\frac{9}{13}.
x=1
Solve x=-\frac{2}{13}\left(-\frac{10}{3}+\frac{4}{3}x\right)+\frac{9}{13} for x.
y=-\frac{10}{3}+\frac{4}{3}\times 1
Substitute 1 for x in the equation y=-\frac{10}{3}+\frac{4}{3}x.
y=-2
Calculate y from y=-\frac{10}{3}+\frac{4}{3}\times 1.
z=2\times 1
Substitute 1 for x in the equation z=2x.
z=2
Calculate z from z=2\times 1.
x=1 y=-2 z=2
The system is now solved.
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