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

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

Solve for x, y

$$x=\frac{7}{10}=0.7$$

$$y = \frac{6}{5} = 1\frac{1}{5} = 1.2$$

Solution Steps

Consider the second equation. Combine 3y and 2y to get 5y.

$$5y=6$$

Divide both sides by 5.

$$y=\frac{6}{5}$$

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

$$2x+3\times \frac{6}{5}=5$$

Multiply 3 and \frac{6}{5} to get \frac{18}{5}.

$$2x+\frac{18}{5}=5$$

Subtract \frac{18}{5} from both sides.

$$2x=5-\frac{18}{5}$$

Subtract \frac{18}{5} from 5 to get \frac{7}{5}.

$$2x=\frac{7}{5}$$

Divide both sides by 2.

$$x=\frac{\frac{7}{5}}{2}$$

Express \frac{\frac{7}{5}}{2} as a single fraction.

$$x=\frac{7}{5\times 2}$$

Multiply 5 and 2 to get 10.

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

The system is now solved.

$$x=\frac{7}{10} y=\frac{6}{5}$$