Solve {l}{3x-5=y-z}{y-8x=5z}{z=9}

$$\left\{ \begin{array} { l } { 3 x - 5 = y - z } \\ { y - 8 x = 5 z } \\ { z = 9 } \end{array} \right.$$

Solve for x, y, z

$$x = -\frac{41}{5} = -8\frac{1}{5} = -8.2$$

$$y = -\frac{103}{5} = -20\frac{3}{5} = -20.6$$

$$z=9$$

Short Steps Using Substitution

Reorder the equations.

$$z=9 y-8x=5z 3x-5=y-z$$

Substitute 9 for z in the second and third equation.

$$y-8x=5\times 9 3x-5=y-9$$

Solve these equations for y and x respectively.

$$y=8x+45 x=-\frac{4}{3}+\frac{1}{3}y$$

Substitute 8x+45 for y in the equation x=-\frac{4}{3}+\frac{1}{3}y.

$$x=-\frac{4}{3}+\frac{1}{3}\left(8x+45\right)$$

Solve x=-\frac{4}{3}+\frac{1}{3}\left(8x+45\right) for x.

$$x=-\frac{41}{5}$$

Substitute -\frac{41}{5} for x in the equation y=8x+45.

$$y=8\left(-\frac{41}{5}\right)+45$$

Calculate y from y=8\left(-\frac{41}{5}\right)+45.

$$y=-\frac{103}{5}$$

The system is now solved.

$$x=-\frac{41}{5} y=-\frac{103}{5} z=9$$