Solve {l}{x+2y=m}{x-y=4}{3x+2y=2}

$$\left\{ \begin{array} { l } { x + 2 y = m } \\ { x - y = 4 } \\ { 3 x + 2 y = 2 } \end{array} \right.$$

Solve for x, y, m

$$x=2$$

$$y=-2$$

$$m=-2$$

Short Steps Using Substitution

Solve x+2y=m for m.

$$m=x+2y$$

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

$$y=x-4 x=\frac{2}{3}-\frac{2}{3}y$$

Substitute x-4 for y in the equation x=\frac{2}{3}-\frac{2}{3}y.

$$x=\frac{2}{3}-\frac{2}{3}\left(x-4\right)$$

Solve x=\frac{2}{3}-\frac{2}{3}\left(x-4\right) for x.

$$x=2$$

Substitute 2 for x in the equation y=x-4.

$$y=2-4$$

Calculate y from y=2-4.

$$y=-2$$

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

$$m=2+2\left(-2\right)$$

Calculate m from m=2+2\left(-2\right).

$$m=-2$$

The system is now solved.

$$x=2 y=-2 m=-2$$