Solve {l}{5x+5x=46}{7x+8y=5}

$$\left\{ \begin{array} { l } { 5 x + 5 x = 46 } \\ { 7 x + 8 y = 5 } \end{array} \right.$$

Solve for x, y

$$x = \frac{23}{5} = 4\frac{3}{5} = 4.6$$

$$y = -\frac{17}{5} = -3\frac{2}{5} = -3.4$$

Solution Steps

Consider the first equation. Combine 5x and 5x to get 10x.

$$10x=46$$

Divide both sides by 10.

$$x=\frac{46}{10}$$

Reduce the fraction \frac{46}{10} to lowest terms by extracting and canceling out 2.

$$x=\frac{23}{5}$$

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

$$7\times \frac{23}{5}+8y=5$$

Multiply 7 and \frac{23}{5} to get \frac{161}{5}.

$$\frac{161}{5}+8y=5$$

Subtract \frac{161}{5} from both sides.

$$8y=5-\frac{161}{5}$$

Subtract \frac{161}{5} from 5 to get -\frac{136}{5}.

$$8y=-\frac{136}{5}$$

Divide both sides by 8.

$$y=\frac{-\frac{136}{5}}{8}$$

Express \frac{-\frac{136}{5}}{8} as a single fraction.

$$y=\frac{-136}{5\times 8}$$

Multiply 5 and 8 to get 40.

$$y=\frac{-136}{40}$$

Reduce the fraction \frac{-136}{40} to lowest terms by extracting and canceling out 8.

$$y=-\frac{17}{5}$$

The system is now solved.

$$x=\frac{23}{5} y=-\frac{17}{5}$$