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

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

Solve for x, y

$$x=\frac{2}{3}\approx 0.666666667$$

$$y = -\frac{14}{9} = -1\frac{5}{9} \approx -1.555555556$$

Solution Steps

Consider the second equation. Combine x and 2x to get 3x.

$$3x=2$$

Divide both sides by 3.

$$x=\frac{2}{3}$$

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

$$2\times \frac{2}{3}-3y=6$$

Multiply 2 and \frac{2}{3} to get \frac{4}{3}.

$$\frac{4}{3}-3y=6$$

Subtract \frac{4}{3} from both sides.

$$-3y=6-\frac{4}{3}$$

Subtract \frac{4}{3} from 6 to get \frac{14}{3}.

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

Divide both sides by -3.

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

Express \frac{\frac{14}{3}}{-3} as a single fraction.

$$y=\frac{14}{3\left(-3\right)}$$

Multiply 3 and -3 to get -9.

$$y=\frac{14}{-9}$$

Fraction \frac{14}{-9} can be rewritten as -\frac{14}{9} by extracting the negative sign.

$$y=-\frac{14}{9}$$

The system is now solved.

$$x=\frac{2}{3} y=-\frac{14}{9}$$