\left\{ \begin{array} { l } { x - 2 y = 0 } \\ { y + z = 0 } \\ { 2 x + y - z - 6 = 0 } \end{array} \right.
Solve for x, y, z
x=2
y=1
z=-1
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x=2y
Solve x-2y=0 for x.
2\times 2y+y-z-6=0
Substitute 2y for x in the equation 2x+y-z-6=0.
y=-z z=5y-6
Solve the second equation for y and the third equation for z.
z=5\left(-1\right)z-6
Substitute -z for y in the equation z=5y-6.
z=-1
Solve z=5\left(-1\right)z-6 for z.
y=-\left(-1\right)
Substitute -1 for z in the equation y=-z.
y=1
Calculate y from y=-\left(-1\right).
x=2\times 1
Substitute 1 for y in the equation x=2y.
x=2
Calculate x from x=2\times 1.
x=2 y=1 z=-1
The system is now solved.
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