Solve {l}{3y=61}{y+2x=1}

$$\left. \begin{array} { l } { 3 y = 61 } \\ { y + 2 x = 1 } \end{array} \right.$$

Solve for y, x

$$x = -\frac{29}{3} = -9\frac{2}{3} \approx -9.666666667$$

$$y = \frac{61}{3} = 20\frac{1}{3} \approx 20.333333333$$

Solution Steps

Consider the first equation. Divide both sides by 3.

$$y=\frac{61}{3}$$

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

$$\frac{61}{3}+2x=1$$

Subtract \frac{61}{3} from both sides.

$$2x=1-\frac{61}{3}$$

Subtract \frac{61}{3} from 1 to get -\frac{58}{3}.

$$2x=-\frac{58}{3}$$

Divide both sides by 2.

$$x=\frac{-\frac{58}{3}}{2}$$

Express \frac{-\frac{58}{3}}{2} as a single fraction.

$$x=\frac{-58}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$x=\frac{-58}{6}$$

Reduce the fraction \frac{-58}{6} to lowest terms by extracting and canceling out 2.

$$x=-\frac{29}{3}$$

The system is now solved.

$$y=\frac{61}{3} x=-\frac{29}{3}$$