Solve {l}{x+y=130}{04x+.65y=78}

$$\left. \begin{array} { l } { x + y = 130 } \\ { 04 x + .65 y = 78 } \end{array} \right.$$

Solve for x, y

$$x=10$$

$$y=120$$

Solution Steps

Consider the second equation. Multiply 0 and 4 to get 0.

$$0x+0.65y=78$$

Anything times zero gives zero.

$$0+0.65y=78$$

Anything plus zero gives itself.

$$0.65y=78$$

Divide both sides by 0.65.

$$y=\frac{78}{0.65}$$

Expand \frac{78}{0.65} by multiplying both numerator and the denominator by 100.

$$y=\frac{7800}{65}$$

Divide 7800 by 65 to get 120.

$$y=120$$

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

$$x+120=130$$

Subtract 120 from both sides.

$$x=130-120$$

Subtract 120 from 130 to get 10.

$$x=10$$

The system is now solved.

$$x=10 y=120$$