Solve {l}{x+y=220}{2/5x=3/8x-5}

$$\left\{ \begin{array} { l } { x + y = 220 } \\ { \frac { 2 } { 5 } x = \frac { 3 } { 8 } x - 5 } \end{array} \right.$$

Solve for x, y

$$x=-200$$

$$y=420$$

Solution Steps

Consider the second equation. Subtract \frac{3}{8}x from both sides.

$$\frac{2}{5}x-\frac{3}{8}x=-5$$

Combine \frac{2}{5}x and -\frac{3}{8}x to get \frac{1}{40}x.

$$\frac{1}{40}x=-5$$

Multiply both sides by 40, the reciprocal of \frac{1}{40}.

$$x=-5\times 40$$

Multiply -5 and 40 to get -200.

$$x=-200$$

Consider the first equation. Insert the known values of variables into the equation.

$$-200+y=220$$

Add 200 to both sides.

$$y=220+200$$

Add 220 and 200 to get 420.

$$y=420$$

The system is now solved.

$$x=-200 y=420$$