\left\{ \begin{array} { c } { x + y + z = 0 } \\ { 2 x - 5 y - 3 z = 10 } \\ { 4 x + 8 y + 2 z = 4 } \end{array} \right.
Solve for x, y, z
x=2
y=0
z=-2
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x=-y-z
Solve x+y+z=0 for x.
2\left(-y-z\right)-5y-3z=10 4\left(-y-z\right)+8y+2z=4
Substitute -y-z for x in the second and third equation.
y=-\frac{10}{7}-\frac{5}{7}z z=-2+2y
Solve these equations for y and z respectively.
z=-2+2\left(-\frac{10}{7}-\frac{5}{7}z\right)
Substitute -\frac{10}{7}-\frac{5}{7}z for y in the equation z=-2+2y.
z=-2
Solve z=-2+2\left(-\frac{10}{7}-\frac{5}{7}z\right) for z.
y=-\frac{10}{7}-\frac{5}{7}\left(-2\right)
Substitute -2 for z in the equation y=-\frac{10}{7}-\frac{5}{7}z.
y=0
Calculate y from y=-\frac{10}{7}-\frac{5}{7}\left(-2\right).
x=-0-\left(-2\right)
Substitute 0 for y and -2 for z in the equation x=-y-z.
x=2
Calculate x from x=-0-\left(-2\right).
x=2 y=0 z=-2
The system is now solved.
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