Solve {l}{15/4=b}{0=5k+b}

$$\left\{ \begin{array} { l } { \frac { 15 } { 4 } = b } \\ { 0 = 5 k + b } \end{array} \right.$$

Solve for b, k

$$b = \frac{15}{4} = 3\frac{3}{4} = 3.75$$

$$k=-\frac{3}{4}=-0.75$$

Solution Steps

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

$$b=\frac{15}{4}$$

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

$$0=5k+\frac{15}{4}$$

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

$$5k+\frac{15}{4}=0$$

Subtract \frac{15}{4} from both sides. Anything subtracted from zero gives its negation.

$$5k=-\frac{15}{4}$$

Divide both sides by 5.

$$k=\frac{-\frac{15}{4}}{5}$$

Express \frac{-\frac{15}{4}}{5} as a single fraction.

$$k=\frac{-15}{4\times 5}$$

Multiply 4 and 5 to get 20.

$$k=\frac{-15}{20}$$

Reduce the fraction \frac{-15}{20} to lowest terms by extracting and canceling out 5.

$$k=-\frac{3}{4}$$

The system is now solved.

$$b=\frac{15}{4} k=-\frac{3}{4}$$