Solve {l}{x+3y+7x+3y=90}{4x+12+7x+21=90}

$$\left. \begin{array} { l } { x + 3 y + 7 x + 3 y = 90 } \\ { 4 x + 12 + 7 x + 21 = 90 } \end{array} \right.$$

Solve for x, y

$$x = \frac{57}{11} = 5\frac{2}{11} \approx 5.181818182$$

$$y = \frac{89}{11} = 8\frac{1}{11} \approx 8.090909091$$

Solution Steps

Consider the second equation. Combine 4x and 7x to get 11x.

$$11x+12+21=90$$

Add 12 and 21 to get 33.

$$11x+33=90$$

Subtract 33 from both sides.

$$11x=90-33$$

Subtract 33 from 90 to get 57.

$$11x=57$$

Divide both sides by 11.

$$x=\frac{57}{11}$$

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

$$\frac{57}{11}+3y+7\times \frac{57}{11}+3y=90$$

Multiply 7 and \frac{57}{11} to get \frac{399}{11}.

$$\frac{57}{11}+3y+\frac{399}{11}+3y=90$$

Add \frac{57}{11} and \frac{399}{11} to get \frac{456}{11}.

$$\frac{456}{11}+3y+3y=90$$

Combine 3y and 3y to get 6y.

$$\frac{456}{11}+6y=90$$

Subtract \frac{456}{11} from both sides.

$$6y=90-\frac{456}{11}$$

Subtract \frac{456}{11} from 90 to get \frac{534}{11}.

$$6y=\frac{534}{11}$$

Divide both sides by 6.

$$y=\frac{\frac{534}{11}}{6}$$

Express \frac{\frac{534}{11}}{6} as a single fraction.

$$y=\frac{534}{11\times 6}$$

Multiply 11 and 6 to get 66.

$$y=\frac{534}{66}$$

Reduce the fraction \frac{534}{66} to lowest terms by extracting and canceling out 6.

$$y=\frac{89}{11}$$

The system is now solved.

$$x=\frac{57}{11} y=\frac{89}{11}$$