\left\{ \begin{array} { c } { y = 2 x + 3 z } \\ { z = 7 x + 8 y } \\ { x = 5 y + 6 z } \end{array} \right.
Solve for y, x, z
x=0
y=0
z=0
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z=7x+8\left(2x+3z\right) x=5\left(2x+3z\right)+6z
Substitute 2x+3z for y in the second and third equation.
x=-z z=-\frac{3}{7}x
Solve these equations for x and z respectively.
z=-\frac{3}{7}\left(-1\right)z
Substitute -z for x in the equation z=-\frac{3}{7}x.
z=0
Solve z=-\frac{3}{7}\left(-1\right)z for z.
x=-0
Substitute 0 for z in the equation x=-z.
x=0
Calculate x from x=-0.
y=2\times 0+3\times 0
Substitute 0 for x and 0 for z in the equation y=2x+3z.
y=0
Calculate y from y=2\times 0+3\times 0.
y=0 x=0 z=0
The system is now solved.
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