Solve for x, y, z
x=-6
y=3
z=2
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x=-y-2z+1
Solve x+y+2z=1 for x.
-y-2z+1+2y-z=-2 -y-2z+1+3y+z=5
Substitute -y-2z+1 for x in the second and third equation.
y=-3+3z z=-4+2y
Solve these equations for y and z respectively.
z=-4+2\left(-3+3z\right)
Substitute -3+3z for y in the equation z=-4+2y.
z=2
Solve z=-4+2\left(-3+3z\right) for z.
y=-3+3\times 2
Substitute 2 for z in the equation y=-3+3z.
y=3
Calculate y from y=-3+3\times 2.
x=-3-2\times 2+1
Substitute 3 for y and 2 for z in the equation x=-y-2z+1.
x=-6
Calculate x from x=-3-2\times 2+1.
x=-6 y=3 z=2
The system is now solved.
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