Solve {l}{30=0k+b}{15=50k+b}

$$\left\{ \begin{array} { l } { 30 = 0 k + b } \\ { 15 = 50 k + b } \end{array} \right.$$

Solve for k, b

$$k=-\frac{3}{10}=-0.3$$

$$b=30$$

Solution Steps

Consider the first equation. Anything times zero gives zero.

$$30=0+b$$

Anything plus zero gives itself.

$$30=b$$

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

$$b=30$$

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

$$15=50k+30$$

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

$$50k+30=15$$

Subtract 30 from both sides.

$$50k=15-30$$

Subtract 30 from 15 to get -15.

$$50k=-15$$

Divide both sides by 50.

$$k=\frac{-15}{50}$$

Reduce the fraction \frac{-15}{50} to lowest terms by extracting and canceling out 5.

$$k=-\frac{3}{10}$$

The system is now solved.

$$k=-\frac{3}{10} b=30$$