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Solve for x, y, z
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x=-y-z
Solve x+y+z=0 for x.
-y-z+y=3 -y-z+z=-2
Substitute -y-z for x in the second and third equation.
z=-3 y=2
Solve these equations for z and y respectively.
x=-2-\left(-3\right)
Substitute -3 for z and 2 for y in the equation x=-y-z.
x=1
Calculate x from x=-2-\left(-3\right).
x=1 y=2 z=-3
The system is now solved.