Solve {l}{x=y}{y=5z}{z+y=1}

$$\left\{ \begin{array} { l } { x = y } \\ { y = 5 z } \\ { z + y = 1 } \end{array} \right.$$

Solve for x, y, z

$$x=\frac{5}{6}\approx 0.833333333$$

$$y=\frac{5}{6}\approx 0.833333333$$

$$z=\frac{1}{6}\approx 0.166666667$$

Short Steps Using Substitution

Solve z+y=1 for z.

$$z=-y+1$$

Substitute 5z for y in the equation z=-y+1.

$$z=-5z+1$$

Solve z=-5z+1 for z.

$$z=\frac{1}{6}$$

Substitute \frac{1}{6} for z in the equation y=5z.

$$y=5\times \frac{1}{6}$$

Calculate y from y=5\times \frac{1}{6}.

$$y=\frac{5}{6}$$

Substitute \frac{5}{6} for y in the equation x=y.

$$x=\frac{5}{6}$$

The system is now solved.

$$x=\frac{5}{6} y=\frac{5}{6} z=\frac{1}{6}$$