Solve {l}{+y+z=1}{x=2y}{z=4y}

$$\left. \begin{array} { l } { + y + z = 1 } \\ { x = 2 y } \\ { z = 4 y } \end{array} \right.$$

Solve for y, z, x

$$x=\frac{2}{5}=0.4$$

$$y=\frac{1}{5}=0.2$$

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

Short Steps Using Substitution

Reorder the equations.

$$x=2y y+z=1 z=4y$$

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

$$z=-y+1 y=\frac{1}{4}z$$

Substitute -y+1 for z in the equation y=\frac{1}{4}z.

$$y=\frac{1}{4}\left(-y+1\right)$$

Solve y=\frac{1}{4}\left(-y+1\right) for y.

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

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

$$z=-\frac{1}{5}+1$$

Calculate z from z=-\frac{1}{5}+1.

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

Substitute \frac{1}{5} for y in the equation x=2y.

$$x=2\times \frac{1}{5}$$

Calculate x from x=2\times \frac{1}{5}.

$$x=\frac{2}{5}$$

The system is now solved.

$$y=\frac{1}{5} z=\frac{4}{5} x=\frac{2}{5}$$