Solve {l}{47+7y=195}{3x+4y=19}

$$\left\{ \begin{array} { l } { 47 + 7 y = 195 } \\ { 3 x + 4 y = 19 } \end{array} \right.$$

Solve for y, x

$$x = -\frac{153}{7} = -21\frac{6}{7} \approx -21.857142857$$

$$y = \frac{148}{7} = 21\frac{1}{7} \approx 21.142857143$$

Solution Steps

Consider the first equation. Subtract 47 from both sides.

$$7y=195-47$$

Subtract 47 from 195 to get 148.

$$7y=148$$

Divide both sides by 7.

$$y=\frac{148}{7}$$

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

$$3x+4\times \frac{148}{7}=19$$

Multiply 4 and \frac{148}{7} to get \frac{592}{7}.

$$3x+\frac{592}{7}=19$$

Subtract \frac{592}{7} from both sides.

$$3x=19-\frac{592}{7}$$

Subtract \frac{592}{7} from 19 to get -\frac{459}{7}.

$$3x=-\frac{459}{7}$$

Divide both sides by 3.

$$x=\frac{-\frac{459}{7}}{3}$$

Express \frac{-\frac{459}{7}}{3} as a single fraction.

$$x=\frac{-459}{7\times 3}$$

Multiply 7 and 3 to get 21.

$$x=\frac{-459}{21}$$

Reduce the fraction \frac{-459}{21} to lowest terms by extracting and canceling out 3.

$$x=-\frac{153}{7}$$

The system is now solved.

$$y=\frac{148}{7} x=-\frac{153}{7}$$