Solve {l}{-x+5y-3z=0}{5x-y-9z=0}{-7x-y+5z=0}

$$\left. \begin{array} { l } { - x + 5 y - 3 z = 0 } \\ { 5 x - y - 9 z = 0 } \\ { - 7 x - y + 5 z = 0 } \end{array} \right.$$

Solve for x, y, z

$$x=0$$

$$y=0$$

$$z=0$$

Short Steps Using Substitution

Solve -x+5y-3z=0 for x.

$$x=5y-3z$$

Substitute 5y-3z for x in the second and third equation.

$$5\left(5y-3z\right)-y-9z=0 -7\left(5y-3z\right)-y+5z=0$$

Solve these equations for y and z respectively.

$$y=z z=\frac{18}{13}y$$

Substitute z for y in the equation z=\frac{18}{13}y.

$$z=\frac{18}{13}z$$

Solve z=\frac{18}{13}z for z.

$$z=0$$

Substitute 0 for z in the equation y=z.

$$y=0$$

Substitute 0 for y and 0 for z in the equation x=5y-3z.

$$x=5\times 0-3\times 0$$

Calculate x from x=5\times 0-3\times 0.

$$x=0$$

The system is now solved.

$$x=0 y=0 z=0$$