Solve {l}{3x+7y=31}{9+3y=31}

$$\left. \begin{array} { l } { 3 x + 7 y = 31 } \\ { 9 + 3 y = 31 } \end{array} \right.$$

Solve for x, y

$$x = -\frac{61}{9} = -6\frac{7}{9} \approx -6.777777778$$

$$y = \frac{22}{3} = 7\frac{1}{3} \approx 7.333333333$$

Solution Steps

Consider the second equation. Subtract 9 from both sides.

$$3y=31-9$$

Subtract 9 from 31 to get 22.

$$3y=22$$

Divide both sides by 3.

$$y=\frac{22}{3}$$

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

$$3x+7\times \frac{22}{3}=31$$

Multiply 7 and \frac{22}{3} to get \frac{154}{3}.

$$3x+\frac{154}{3}=31$$

Subtract \frac{154}{3} from both sides.

$$3x=31-\frac{154}{3}$$

Subtract \frac{154}{3} from 31 to get -\frac{61}{3}.

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

Divide both sides by 3.

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

Express \frac{-\frac{61}{3}}{3} as a single fraction.

$$x=\frac{-61}{3\times 3}$$

Multiply 3 and 3 to get 9.

$$x=\frac{-61}{9}$$

Fraction \frac{-61}{9} can be rewritten as -\frac{61}{9} by extracting the negative sign.

$$x=-\frac{61}{9}$$

The system is now solved.

$$x=-\frac{61}{9} y=\frac{22}{3}$$