Solve {l}{0x+40y=13480}{80x+50y=17690}

$$\left. \begin{array} { l } { 0 x + 40 y = 13480 } \\ { 80 x + 50 y = 17690 } \end{array} \right.$$

Solve for x, y

$$x = \frac{21}{2} = 10\frac{1}{2} = 10.5$$

$$y=337$$

Solution Steps

Consider the first equation. Anything times zero gives zero.

$$0+40y=13480$$

Anything plus zero gives itself.

$$40y=13480$$

Divide both sides by 40.

$$y=\frac{13480}{40}$$

Divide 13480 by 40 to get 337.

$$y=337$$

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

$$80x+50\times 337=17690$$

Multiply 50 and 337 to get 16850.

$$80x+16850=17690$$

Subtract 16850 from both sides.

$$80x=17690-16850$$

Subtract 16850 from 17690 to get 840.

$$80x=840$$

Divide both sides by 80.

$$x=\frac{840}{80}$$

Reduce the fraction \frac{840}{80} to lowest terms by extracting and canceling out 40.

$$x=\frac{21}{2}$$

The system is now solved.

$$x=\frac{21}{2} y=337$$