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

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

Solve for x, y

$$x=\frac{1}{4}=0.25$$

$$y = -\frac{25}{6} = -4\frac{1}{6} \approx -4.166666667$$

Solution Steps

Consider the second equation. Subtract 4 from both sides.

$$4x=5-4$$

Subtract 4 from 5 to get 1.

$$4x=1$$

Divide both sides by 4.

$$x=\frac{1}{4}$$

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

$$2\times \frac{1}{4}-3y=13$$

Multiply 2 and \frac{1}{4} to get \frac{1}{2}.

$$\frac{1}{2}-3y=13$$

Subtract \frac{1}{2} from both sides.

$$-3y=13-\frac{1}{2}$$

Subtract \frac{1}{2} from 13 to get \frac{25}{2}.

$$-3y=\frac{25}{2}$$

Divide both sides by -3.

$$y=\frac{\frac{25}{2}}{-3}$$

Express \frac{\frac{25}{2}}{-3} as a single fraction.

$$y=\frac{25}{2\left(-3\right)}$$

Multiply 2 and -3 to get -6.

$$y=\frac{25}{-6}$$

Fraction \frac{25}{-6} can be rewritten as -\frac{25}{6} by extracting the negative sign.

$$y=-\frac{25}{6}$$

The system is now solved.

$$x=\frac{1}{4} y=-\frac{25}{6}$$