Solve {l}{2x+3x=6}{6x+9y=3}

$$\left. \begin{array} { l } { 2 x + 3 x = 6 } \\ { 6 x + 9 y = 3 } \end{array} \right.$$

Solve for x, y

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

$$y=-\frac{7}{15}\approx -0.466666667$$

Solution Steps

Consider the first equation. Combine 2x and 3x to get 5x.

$$5x=6$$

Divide both sides by 5.

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

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

$$6\times \frac{6}{5}+9y=3$$

Multiply 6 and \frac{6}{5} to get \frac{36}{5}.

$$\frac{36}{5}+9y=3$$

Subtract \frac{36}{5} from both sides.

$$9y=3-\frac{36}{5}$$

Subtract \frac{36}{5} from 3 to get -\frac{21}{5}.

$$9y=-\frac{21}{5}$$

Divide both sides by 9.

$$y=\frac{-\frac{21}{5}}{9}$$

Express \frac{-\frac{21}{5}}{9} as a single fraction.

$$y=\frac{-21}{5\times 9}$$

Multiply 5 and 9 to get 45.

$$y=\frac{-21}{45}$$

Reduce the fraction \frac{-21}{45} to lowest terms by extracting and canceling out 3.

$$y=-\frac{7}{15}$$

The system is now solved.

$$x=\frac{6}{5} y=-\frac{7}{15}$$