Solve for x, y, z
x=3
y=2
z=-4
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x+y+2z=-3 2x+3y+3z=0 3x-y-z=11
Reorder the equations.
x=-y-2z-3
Solve x+y+2z=-3 for x.
2\left(-y-2z-3\right)+3y+3z=0 3\left(-y-2z-3\right)-y-z=11
Substitute -y-2z-3 for x in the second and third equation.
y=z+6 z=-\frac{20}{7}-\frac{4}{7}y
Solve these equations for y and z respectively.
z=-\frac{20}{7}-\frac{4}{7}\left(z+6\right)
Substitute z+6 for y in the equation z=-\frac{20}{7}-\frac{4}{7}y.
z=-4
Solve z=-\frac{20}{7}-\frac{4}{7}\left(z+6\right) for z.
y=-4+6
Substitute -4 for z in the equation y=z+6.
y=2
Calculate y from y=-4+6.
x=-2-2\left(-4\right)-3
Substitute 2 for y and -4 for z in the equation x=-y-2z-3.
x=3
Calculate x from x=-2-2\left(-4\right)-3.
x=3 y=2 z=-4
The system is now solved.
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