Solve {ccc}{1}&{1}&{1}{2}&{3}&{9}{6}&{1}&{8}{l}{x}{y}{z}={c}{0}{0}{0}

$$\left( \begin{array} { c c c } { 1 } & { 1 } & { 1 } \\ { 2 } & { 3 } & { 9 } \\ { 6 } & { 1 } & { 8 } \end{array} \right) \left( \begin{array} { l } { x } \\ { y } \\ { z } \end{array} \right) = \left( \begin{array} { c } { 0 } \\ { 0 } \\ { 0 } \end{array} \right)$$

Solve for x, y, z

$$x=0$$

$$y=0$$

$$z=0$$

Short Steps Using Substitution

Solve x+y+z=0 for x.

$$x=-y-z$$

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

$$2\left(-y-z\right)+3y+9z=0 6\left(-y-z\right)+y+8z=0$$

Solve these equations for y and z respectively.

$$y=-7z z=\frac{5}{2}y$$

Substitute -7z for y in the equation z=\frac{5}{2}y.

$$z=\frac{5}{2}\left(-7\right)z$$

Solve z=\frac{5}{2}\left(-7\right)z for z.

$$z=0$$

Substitute 0 for z in the equation y=-7z.

$$y=-7\times 0$$

Calculate y from y=-7\times 0.

$$y=0$$

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

$$x=-0-0$$

Calculate x from x=-0-0.

$$x=0$$

The system is now solved.

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