Solve {l}{x=z15-60/150}{y=2150-90/150}{z=x+y}

$$\left. \begin{array} { l } { x = z \frac { 15 - 60 } { 150 } } \\ { y = 2 \frac { 150 - 90 } { 150 } } \\ { z = x + y } \end{array} \right.$$

Solve for x, z, y

$$x=-\frac{12}{65}\approx -0.184615385$$

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

$$z=\frac{8}{13}\approx 0.615384615$$

Short Steps Using Substitution

Multiply each equation by the least common multiple of denominators in it. Simplify.

$$150x=-45z y=\frac{4}{5} z=x+y$$

Reorder the equations.

$$y=\frac{4}{5} 150x=-45z z=x+y$$

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

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

Solve the second equation for z and the third equation for x.

$$z=-\frac{10}{3}x x=z-\frac{4}{5}$$

Substitute -\frac{10}{3}x for z in the equation x=z-\frac{4}{5}.

$$x=-\frac{10}{3}x-\frac{4}{5}$$

Solve x=-\frac{10}{3}x-\frac{4}{5} for x.

$$x=-\frac{12}{65}$$

Substitute -\frac{12}{65} for x in the equation z=-\frac{10}{3}x.

$$z=-\frac{10}{3}\left(-\frac{12}{65}\right)$$

Calculate z from z=-\frac{10}{3}\left(-\frac{12}{65}\right).

$$z=\frac{8}{13}$$

The system is now solved.

$$x=-\frac{12}{65} z=\frac{8}{13} y=\frac{4}{5}$$