Solve {l}{230+0.1k=c}{150+0.22k=0}

$$\left\{ \begin{array} { l } { 230 + 0.1 k = c } \\ { 150 + 0.22 k = 0 } \end{array} \right.$$

Solve for k, c

$$k = -\frac{7500}{11} = -681\frac{9}{11} \approx -681.818181818$$

$$c = \frac{1780}{11} = 161\frac{9}{11} \approx 161.818181818$$

Solution Steps

Consider the second equation. Subtract 150 from both sides. Anything subtracted from zero gives its negation.

$$0.22k=-150$$

Divide both sides by 0.22.

$$k=\frac{-150}{0.22}$$

Expand \frac{-150}{0.22} by multiplying both numerator and the denominator by 100.

$$k=\frac{-15000}{22}$$

Reduce the fraction \frac{-15000}{22} to lowest terms by extracting and canceling out 2.

$$k=-\frac{7500}{11}$$

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

$$230+0.1\left(-\frac{7500}{11}\right)=c$$

Multiply 0.1 and -\frac{7500}{11} to get -\frac{750}{11}.

$$230-\frac{750}{11}=c$$

Subtract \frac{750}{11} from 230 to get \frac{1780}{11}.

$$\frac{1780}{11}=c$$

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

$$c=\frac{1780}{11}$$

The system is now solved.

$$k=-\frac{7500}{11} c=\frac{1780}{11}$$