Solve {r}{-2=3k+9}{6=-1k+r}

$$\left. \begin{array} { r } { - 2 = 3 k + 9 } \\ { 6 = - 1 k + r } \end{array} \right.$$

Solve for k, r

$$r = \frac{7}{3} = 2\frac{1}{3} \approx 2.333333333$$

$$k = -\frac{11}{3} = -3\frac{2}{3} \approx -3.666666667$$

Solution Steps

Consider the first equation. Swap sides so that all variable terms are on the left hand side.

$$3k+9=-2$$

Subtract 9 from both sides.

$$3k=-2-9$$

Subtract 9 from -2 to get -11.

$$3k=-11$$

Divide both sides by 3.

$$k=-\frac{11}{3}$$

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

$$6=-\left(-\frac{11}{3}\right)+r$$

Multiply -1 and -\frac{11}{3} to get \frac{11}{3}.

$$6=\frac{11}{3}+r$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{11}{3}+r=6$$

Subtract \frac{11}{3} from both sides.

$$r=6-\frac{11}{3}$$

Subtract \frac{11}{3} from 6 to get \frac{7}{3}.

$$r=\frac{7}{3}$$

The system is now solved.

$$k=-\frac{11}{3} r=\frac{7}{3}$$