Solve {l}{180k+6=100}{220k+b=80}

$$\left\{ \begin{array} { l } { 180 k + 6 = 100 } \\ { 220 k + b = 80 } \end{array} \right.$$

Solve for k, b

$$k=\frac{47}{90}\approx 0.522222222$$

$$b = -\frac{314}{9} = -34\frac{8}{9} \approx -34.888888889$$

Solution Steps

Consider the first equation. Subtract 6 from both sides.

$$180k=100-6$$

Subtract 6 from 100 to get 94.

$$180k=94$$

Divide both sides by 180.

$$k=\frac{94}{180}$$

Reduce the fraction \frac{94}{180} to lowest terms by extracting and canceling out 2.

$$k=\frac{47}{90}$$

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

$$220\times \frac{47}{90}+b=80$$

Multiply 220 and \frac{47}{90} to get \frac{1034}{9}.

$$\frac{1034}{9}+b=80$$

Subtract \frac{1034}{9} from both sides.

$$b=80-\frac{1034}{9}$$

Subtract \frac{1034}{9} from 80 to get -\frac{314}{9}.

$$b=-\frac{314}{9}$$

The system is now solved.

$$k=\frac{47}{90} b=-\frac{314}{9}$$