Solve {l}{2x-y=3}{2x+x=14}

$$\left. \begin{array} { l } { 2 x - y = 3 } \\ { 2 x + x = 14 } \end{array} \right.$$

Solve for x, y

$$x = \frac{14}{3} = 4\frac{2}{3} \approx 4.666666667$$

$$y = \frac{19}{3} = 6\frac{1}{3} \approx 6.333333333$$

Solution Steps

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

$$3x=14$$

Divide both sides by 3.

$$x=\frac{14}{3}$$

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

$$2\times \frac{14}{3}-y=3$$

Multiply 2 and \frac{14}{3} to get \frac{28}{3}.

$$\frac{28}{3}-y=3$$

Subtract \frac{28}{3} from both sides.

$$-y=3-\frac{28}{3}$$

Subtract \frac{28}{3} from 3 to get -\frac{19}{3}.

$$-y=-\frac{19}{3}$$

Divide both sides by -1.

$$y=\frac{-\frac{19}{3}}{-1}$$

Express \frac{-\frac{19}{3}}{-1} as a single fraction.

$$y=\frac{-19}{3\left(-1\right)}$$

Multiply 3 and -1 to get -3.

$$y=\frac{-19}{-3}$$

Fraction \frac{-19}{-3} can be simplified to \frac{19}{3} by removing the negative sign from both the numerator and the denominator.

$$y=\frac{19}{3}$$

The system is now solved.

$$x=\frac{14}{3} y=\frac{19}{3}$$