Solve {l}{1x+y=250}{x/19+5/10=18}

$$\left. \begin{array} { l } { 1 x + y = 250 } \\ { \frac { x } { 19 } + \frac { 5 } { 10 } = 18 } \end{array} \right.$$

Solve for x, y

$$x = \frac{665}{2} = 332\frac{1}{2} = 332.5$$

$$y = -\frac{165}{2} = -82\frac{1}{2} = -82.5$$

Solution Steps

Consider the second equation. Multiply both sides of the equation by 190, the least common multiple of 19,10.

$$10x+19\times 5=3420$$

Multiply 19 and 5 to get 95.

$$10x+95=3420$$

Subtract 95 from both sides.

$$10x=3420-95$$

Subtract 95 from 3420 to get 3325.

$$10x=3325$$

Divide both sides by 10.

$$x=\frac{3325}{10}$$

Reduce the fraction \frac{3325}{10} to lowest terms by extracting and canceling out 5.

$$x=\frac{665}{2}$$

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

$$1\times \frac{665}{2}+y=250$$

Multiply 1 and \frac{665}{2} to get \frac{665}{2}.

$$\frac{665}{2}+y=250$$

Subtract \frac{665}{2} from both sides.

$$y=250-\frac{665}{2}$$

Subtract \frac{665}{2} from 250 to get -\frac{165}{2}.

$$y=-\frac{165}{2}$$

The system is now solved.

$$x=\frac{665}{2} y=-\frac{165}{2}$$