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