Solve {l}{6x-y-9z=5}{4x+y-z=6}{8x+y-8z=8}

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

Solve for x, y, z

$$x = \frac{19}{10} = 1\frac{9}{10} = 1.9$$

$$y=-\frac{4}{5}=-0.8$$

$$z=\frac{4}{5}=0.8$$

Short Steps Using Substitution

Solve 6x-y-9z=5 for y.

$$y=6x-9z-5$$

Substitute 6x-9z-5 for y in the second and third equation.

$$4x+6x-9z-5-z=6 8x+6x-9z-5-8z=8$$

Solve these equations for x and z respectively.

$$x=z+\frac{11}{10} z=\frac{14}{17}x-\frac{13}{17}$$

Substitute z+\frac{11}{10} for x in the equation z=\frac{14}{17}x-\frac{13}{17}.

$$z=\frac{14}{17}\left(z+\frac{11}{10}\right)-\frac{13}{17}$$

Solve z=\frac{14}{17}\left(z+\frac{11}{10}\right)-\frac{13}{17} for z.

$$z=\frac{4}{5}$$

Substitute \frac{4}{5} for z in the equation x=z+\frac{11}{10}.

$$x=\frac{4}{5}+\frac{11}{10}$$

Calculate x from x=\frac{4}{5}+\frac{11}{10}.

$$x=\frac{19}{10}$$

Substitute \frac{19}{10} for x and \frac{4}{5} for z in the equation y=6x-9z-5.

$$y=6\times \frac{19}{10}-9\times \frac{4}{5}-5$$

Calculate y from y=6\times \frac{19}{10}-9\times \frac{4}{5}-5.

$$y=-\frac{4}{5}$$

The system is now solved.

$$x=\frac{19}{10} y=-\frac{4}{5} z=\frac{4}{5}$$