Solve {l}{2x-y=4m+3}{2y-x=-3}{x+y=0}

$$\left\{ \begin{array} { l } { 2 x - y = 4 m + 3 } \\ { 2 y - x = - 3 } \\ { x + y = 0 } \end{array} \right.$$

Solve for x, y, m

$$x=1$$

$$y=-1$$

$$m=0$$

Short Steps Using Substitution

Solve 2x-y=4m+3 for y.

$$y=2x-4m-3$$

Substitute 2x-4m-3 for y in the second and third equation.

$$2\left(2x-4m-3\right)-x=-3 x+2x-4m-3=0$$

Solve these equations for x and m respectively.

$$x=\frac{8}{3}m+1 m=-\frac{3}{4}+\frac{3}{4}x$$

Substitute \frac{8}{3}m+1 for x in the equation m=-\frac{3}{4}+\frac{3}{4}x.

$$m=-\frac{3}{4}+\frac{3}{4}\left(\frac{8}{3}m+1\right)$$

Solve m=-\frac{3}{4}+\frac{3}{4}\left(\frac{8}{3}m+1\right) for m.

$$m=0$$

Substitute 0 for m in the equation x=\frac{8}{3}m+1.

$$x=\frac{8}{3}\times 0+1$$

Calculate x from x=\frac{8}{3}\times 0+1.

$$x=1$$

Substitute 1 for x and 0 for m in the equation y=2x-4m-3.

$$y=2\times 1-4\times 0-3$$

Calculate y from y=2\times 1-4\times 0-3.

$$y=-1$$

The system is now solved.

$$x=1 y=-1 m=0$$