\left\{ \begin{array} { l } { 2 x + y - z = 0 } \\ { 5 x - y + 2 z = 0 } \\ { x + 2 y + z = 0 } \end{array} \right.
Solve for x, y, z
x=0
y=0
z=0
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y=-2x+z
Solve 2x+y-z=0 for y.
5x-\left(-2x+z\right)+2z=0 x+2\left(-2x+z\right)+z=0
Substitute -2x+z for y in the second and third equation.
x=-\frac{1}{7}z z=x
Solve these equations for x and z respectively.
z=-\frac{1}{7}z
Substitute -\frac{1}{7}z for x in the equation z=x.
z=0
Solve z=-\frac{1}{7}z for z.
x=-\frac{1}{7}\times 0
Substitute 0 for z in the equation x=-\frac{1}{7}z.
x=0
Calculate x from x=-\frac{1}{7}\times 0.
y=-2\times 0+0
Substitute 0 for x and 0 for z in the equation y=-2x+z.
y=0
Calculate y from y=-2\times 0+0.
x=0 y=0 z=0
The system is now solved.
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