Solve {l}{7*+2y=34}{14x+9y=56}

$$\left. \begin{array} { l } { 7 \times + 2 y = 34 } \\ { 14 x + 9 y = 56 } \end{array} \right.$$

Solve for y, x

$$x = \frac{239}{98} = 2\frac{43}{98} \approx 2.43877551$$

$$y = \frac{17}{7} = 2\frac{3}{7} \approx 2.428571429$$

Solution Steps

Consider the first equation. Multiply 7 and 2 to get 14.

$$14y=34$$

Divide both sides by 14.

$$y=\frac{34}{14}$$

Reduce the fraction \frac{34}{14} to lowest terms by extracting and canceling out 2.

$$y=\frac{17}{7}$$

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

$$14x+9\times \frac{17}{7}=56$$

Multiply 9 and \frac{17}{7} to get \frac{153}{7}.

$$14x+\frac{153}{7}=56$$

Subtract \frac{153}{7} from both sides.

$$14x=56-\frac{153}{7}$$

Subtract \frac{153}{7} from 56 to get \frac{239}{7}.

$$14x=\frac{239}{7}$$

Divide both sides by 14.

$$x=\frac{\frac{239}{7}}{14}$$

Express \frac{\frac{239}{7}}{14} as a single fraction.

$$x=\frac{239}{7\times 14}$$

Multiply 7 and 14 to get 98.

$$x=\frac{239}{98}$$

The system is now solved.

$$y=\frac{17}{7} x=\frac{239}{98}$$