Solve {l}{x+2y=3}{3x+5y=m}{x+y=1}

$$\left\{ \begin{array} { l } { x + 2 y = 3 } \\ { 3 x + 5 y = m } \\ { x + y = 1 } \end{array} \right.$$

Solve for x, y, m

$$x=-1$$

$$y=2$$

$$m=7$$

Short Steps Using Substitution

Reorder the equations.

$$3x+5y=m x+2y=3 x+y=1$$

Solve 3x+5y=m for m.

$$m=3x+5y$$

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

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

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

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

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

$$x=-1$$

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

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

Calculate y from y=-\frac{1}{2}\left(-1\right)+\frac{3}{2}.

$$y=2$$

Substitute 2 for y and -1 for x in the equation m=3x+5y.

$$m=3\left(-1\right)+5\times 2$$

Calculate m from m=3\left(-1\right)+5\times 2.

$$m=7$$

The system is now solved.

$$x=-1 y=2 m=7$$