Solve {l}{x+2y=3m}{x-y=9m}{5x+8y=38}

$$\left\{ \begin{array} { l } { x + 2 y = 3 m } \\ { x - y = 9 m } \\ { 5 x + 8 y = 38 } \end{array} \right.$$

Solve for x, y, m

$$x=14$$

$$y=-4$$

$$m=2$$

Short Steps Using Substitution

Solve x+2y=3m for x.

$$x=-2y+3m$$

Substitute -2y+3m for x in the second and third equation.

$$-2y+3m-y=9m 5\left(-2y+3m\right)+8y=38$$

Solve these equations for y and m respectively.

$$y=-2m m=\frac{38}{15}+\frac{2}{15}y$$

Substitute -2m for y in the equation m=\frac{38}{15}+\frac{2}{15}y.

$$m=\frac{38}{15}+\frac{2}{15}\left(-2\right)m$$

Solve m=\frac{38}{15}+\frac{2}{15}\left(-2\right)m for m.

$$m=2$$

Substitute 2 for m in the equation y=-2m.

$$y=-2\times 2$$

Calculate y from y=-2\times 2.

$$y=-4$$

Substitute -4 for y and 2 for m in the equation x=-2y+3m.

$$x=-2\left(-4\right)+3\times 2$$

Calculate x from x=-2\left(-4\right)+3\times 2.

$$x=14$$

The system is now solved.

$$x=14 y=-4 m=2$$