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

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

Solve for y, x

$$x=-8$$

$$y = -\frac{13}{2} = -6\frac{1}{2} = -6.5$$

Solution Steps

Consider the first equation. Combine y and -3y to get -2y.

$$-2y=13$$

Divide both sides by -2.

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

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

$$x-2\left(-\frac{13}{2}\right)=5$$

Multiply -2 and -\frac{13}{2} to get 13.

$$x+13=5$$

Subtract 13 from both sides.

$$x=5-13$$

Subtract 13 from 5 to get -8.

$$x=-8$$

The system is now solved.

$$y=-\frac{13}{2} x=-8$$