Solve {l}{6x-5=8}{2x+4y=14}

$$\left. \begin{array} { l } { 6 x - 5 = 8 } \\ { 2 x + 4 y = 14 } \end{array} \right.$$

Solve for x, y

$$x = \frac{13}{6} = 2\frac{1}{6} \approx 2.166666667$$

$$y = \frac{29}{12} = 2\frac{5}{12} \approx 2.416666667$$

Solution Steps

Consider the first equation. Add 5 to both sides.

$$6x=8+5$$

Add 8 and 5 to get 13.

$$6x=13$$

Divide both sides by 6.

$$x=\frac{13}{6}$$

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

$$2\times \frac{13}{6}+4y=14$$

Multiply 2 and \frac{13}{6} to get \frac{13}{3}.

$$\frac{13}{3}+4y=14$$

Subtract \frac{13}{3} from both sides.

$$4y=14-\frac{13}{3}$$

Subtract \frac{13}{3} from 14 to get \frac{29}{3}.

$$4y=\frac{29}{3}$$

Divide both sides by 4.

$$y=\frac{\frac{29}{3}}{4}$$

Express \frac{\frac{29}{3}}{4} as a single fraction.

$$y=\frac{29}{3\times 4}$$

Multiply 3 and 4 to get 12.

$$y=\frac{29}{12}$$

The system is now solved.

$$x=\frac{13}{6} y=\frac{29}{12}$$