Solve {l}{3x+4y+6z=0}{6x+7y+8z=0}{9x+11y+5z=0}

$$\left\{ \begin{array} { l } { 3 x + 4 y + 6 z = 0 } \\ { 6 x + 7 y + 8 z = 0 } \\ { 9 x + 11 y + 5 z = 0 } \end{array} \right.$$

Solve for x, y, z

$$x=0$$

$$y=0$$

$$z=0$$

Short Steps Using Substitution

Solve 3x+4y+6z=0 for x.

$$x=-\frac{4}{3}y-2z$$

Substitute -\frac{4}{3}y-2z for x in the second and third equation.

$$6\left(-\frac{4}{3}y-2z\right)+7y+8z=0 9\left(-\frac{4}{3}y-2z\right)+11y+5z=0$$

Solve these equations for y and z respectively.

$$y=-4z z=-\frac{1}{13}y$$

Substitute -4z for y in the equation z=-\frac{1}{13}y.

$$z=-\frac{1}{13}\left(-4\right)z$$

Solve z=-\frac{1}{13}\left(-4\right)z for z.

$$z=0$$

Substitute 0 for z in the equation y=-4z.

$$y=-4\times 0$$

Calculate y from y=-4\times 0.

$$y=0$$

Substitute 0 for y and 0 for z in the equation x=-\frac{4}{3}y-2z.

$$x=-\frac{4}{3}\times 0-2\times 0$$

Calculate x from x=-\frac{4}{3}\times 0-2\times 0.

$$x=0$$

The system is now solved.

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