Solve {r}{10x+14=460}{x+y=40}

$$\left. \begin{array} { r } { 10 x + 14 = 460 } \\ { x + y = 40 } \end{array} \right.$$

Solve for x, y

$$x = \frac{223}{5} = 44\frac{3}{5} = 44.6$$

$$y = -\frac{23}{5} = -4\frac{3}{5} = -4.6$$

Solution Steps

Consider the first equation. Subtract 14 from both sides.

$$10x=460-14$$

Subtract 14 from 460 to get 446.

$$10x=446$$

Divide both sides by 10.

$$x=\frac{446}{10}$$

Reduce the fraction \frac{446}{10} to lowest terms by extracting and canceling out 2.

$$x=\frac{223}{5}$$

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

$$\frac{223}{5}+y=40$$

Subtract \frac{223}{5} from both sides.

$$y=40-\frac{223}{5}$$

Subtract \frac{223}{5} from 40 to get -\frac{23}{5}.

$$y=-\frac{23}{5}$$

The system is now solved.

$$x=\frac{223}{5} y=-\frac{23}{5}$$