Solve {l}{2x-y=1}{3x=2}

$$\left. \begin{array} { l } { 2 x - y = 1 } \\ { 3 x = 2 } \end{array} \right.$$

Solve for x, y

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

$$y=\frac{1}{3}\approx 0.333333333$$

Solution Steps

Consider the second equation. Divide both sides by 3.

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

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

$$2\times \frac{2}{3}-y=1$$

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

$$\frac{4}{3}-y=1$$

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

$$-y=1-\frac{4}{3}$$

Subtract \frac{4}{3} from 1 to get -\frac{1}{3}.

$$-y=-\frac{1}{3}$$

Divide both sides by -1.

$$y=\frac{-\frac{1}{3}}{-1}$$

Express \frac{-\frac{1}{3}}{-1} as a single fraction.

$$y=\frac{-1}{3\left(-1\right)}$$

Cancel out -1 in both numerator and denominator.

$$y=\frac{1}{3}$$

The system is now solved.

$$x=\frac{2}{3} y=\frac{1}{3}$$