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