Solve {l}{2x-3y=13}{4x+2=5}

$$\left\{ \begin{array} { l } { 2 x - 3 y = 13 } \\ { 4 x + 2 = 5 } \end{array} \right.$$

Solve for x, y

$$x=\frac{3}{4}=0.75$$

$$y = -\frac{23}{6} = -3\frac{5}{6} \approx -3.833333333$$

Solution Steps

Consider the second equation. Subtract 2 from both sides.

$$4x=5-2$$

Subtract 2 from 5 to get 3.

$$4x=3$$

Divide both sides by 4.

$$x=\frac{3}{4}$$

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

$$2\times \frac{3}{4}-3y=13$$

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

$$\frac{3}{2}-3y=13$$

Subtract \frac{3}{2} from both sides.

$$-3y=13-\frac{3}{2}$$

Subtract \frac{3}{2} from 13 to get \frac{23}{2}.

$$-3y=\frac{23}{2}$$

Divide both sides by -3.

$$y=\frac{\frac{23}{2}}{-3}$$

Express \frac{\frac{23}{2}}{-3} as a single fraction.

$$y=\frac{23}{2\left(-3\right)}$$

Multiply 2 and -3 to get -6.

$$y=\frac{23}{-6}$$

Fraction \frac{23}{-6} can be rewritten as -\frac{23}{6} by extracting the negative sign.

$$y=-\frac{23}{6}$$

The system is now solved.

$$x=\frac{3}{4} y=-\frac{23}{6}$$