Solve {l}{x*7=y}{y-108=z}{z:2=x}

$$\left. \begin{array} { l } { x \cdot 7 = y } \\ { y - 108 = z } \\ { z : 2 = x } \end{array} \right.$$

Solve for x, y, z

$$x = \frac{108}{5} = 21\frac{3}{5} = 21.6$$

$$y = \frac{756}{5} = 151\frac{1}{5} = 151.2$$

$$z = \frac{216}{5} = 43\frac{1}{5} = 43.2$$

Short Steps Using Substitution

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

$$x\times 7=y y-108=z z=2x$$

Solve x\times 7=y for y.

$$y=7x$$

Substitute 7x for y in the equation y-108=z.

$$7x-108=z$$

Solve 7x-108=z for x.

$$x=\frac{108}{7}+\frac{1}{7}z$$

Substitute \frac{108}{7}+\frac{1}{7}z for x in the equation z=2x.

$$z=2\left(\frac{108}{7}+\frac{1}{7}z\right)$$

Solve z=2\left(\frac{108}{7}+\frac{1}{7}z\right) for z.

$$z=\frac{216}{5}$$

Substitute \frac{216}{5} for z in the equation x=\frac{108}{7}+\frac{1}{7}z.

$$x=\frac{108}{7}+\frac{1}{7}\times \frac{216}{5}$$

Calculate x from x=\frac{108}{7}+\frac{1}{7}\times \frac{216}{5}.

$$x=\frac{108}{5}$$

Substitute \frac{108}{5} for x in the equation y=7x.

$$y=7\times \frac{108}{5}$$

Calculate y from y=7\times \frac{108}{5}.

$$y=\frac{756}{5}$$

The system is now solved.

$$x=\frac{108}{5} y=\frac{756}{5} z=\frac{216}{5}$$