Solve for x, y, z
x=1
y=-2
z=3
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x=-y-z+2
Solve x+y+z=2 for x.
2\left(-y-z+2\right)+3y+5z=11 -y-z+2-5y+6z=29
Substitute -y-z+2 for x in the second and third equation.
y=-3z+7 z=\frac{27}{5}+\frac{6}{5}y
Solve these equations for y and z respectively.
z=\frac{27}{5}+\frac{6}{5}\left(-3z+7\right)
Substitute -3z+7 for y in the equation z=\frac{27}{5}+\frac{6}{5}y.
z=3
Solve z=\frac{27}{5}+\frac{6}{5}\left(-3z+7\right) for z.
y=-3\times 3+7
Substitute 3 for z in the equation y=-3z+7.
y=-2
Calculate y from y=-3\times 3+7.
x=-\left(-2\right)-3+2
Substitute -2 for y and 3 for z in the equation x=-y-z+2.
x=1
Calculate x from x=-\left(-2\right)-3+2.
x=1 y=-2 z=3
The system is now solved.
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