Solve {l}{2x+3y=10}{6y-2=5}

$$\left. \begin{array} { l } { 2 x + 3 y = 10 } \\ { 6 y - 2 = 5 } \end{array} \right.$$

Solve for x, y

$$x = \frac{13}{4} = 3\frac{1}{4} = 3.25$$

$$y = \frac{7}{6} = 1\frac{1}{6} \approx 1.166666667$$

Solution Steps

Consider the second equation. Add 2 to both sides.

$$6y=5+2$$

Add 5 and 2 to get 7.

$$6y=7$$

Divide both sides by 6.

$$y=\frac{7}{6}$$

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

$$2x+3\times \frac{7}{6}=10$$

Multiply 3 and \frac{7}{6} to get \frac{7}{2}.

$$2x+\frac{7}{2}=10$$

Subtract \frac{7}{2} from both sides.

$$2x=10-\frac{7}{2}$$

Subtract \frac{7}{2} from 10 to get \frac{13}{2}.

$$2x=\frac{13}{2}$$

Divide both sides by 2.

$$x=\frac{\frac{13}{2}}{2}$$

Express \frac{\frac{13}{2}}{2} as a single fraction.

$$x=\frac{13}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$x=\frac{13}{4}$$

The system is now solved.

$$x=\frac{13}{4} y=\frac{7}{6}$$