Solve {l}{x+y+z=66}{x=2y}{3z=2y}

$$\left. \begin{array} { l } { x + y + z = 66 } \\ { x = 2 y } \\ { 3 z = 2 y } \end{array} \right.$$

Solve for x, y, z

$$x=36$$

$$y=18$$

$$z=12$$

Short Steps Using Substitution

Reorder the equations.

$$x=2y x+y+z=66 3z=2y$$

Substitute 2y for x in the equation x+y+z=66.

$$2y+y+z=66$$

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

$$y=-\frac{1}{3}z+22 z=\frac{2}{3}y$$

Substitute -\frac{1}{3}z+22 for y in the equation z=\frac{2}{3}y.

$$z=\frac{2}{3}\left(-\frac{1}{3}z+22\right)$$

Solve z=\frac{2}{3}\left(-\frac{1}{3}z+22\right) for z.

$$z=12$$

Substitute 12 for z in the equation y=-\frac{1}{3}z+22.

$$y=-\frac{1}{3}\times 12+22$$

Calculate y from y=-\frac{1}{3}\times 12+22.

$$y=18$$

Substitute 18 for y in the equation x=2y.

$$x=2\times 18$$

Calculate x from x=2\times 18.

$$x=36$$

The system is now solved.

$$x=36 y=18 z=12$$