Solve {l}{307k+b=5}{318k+6=3}

$$\left\{ \begin{array} { l } { 307 k + b = 5 } \\ { 318 k + 6 = 3 } \end{array} \right.$$

Solve for k, b

$$k=-\frac{1}{106}\approx -0.009433962$$

$$b = \frac{837}{106} = 7\frac{95}{106} \approx 7.896226415$$

Solution Steps

Consider the second equation. Subtract 6 from both sides.

$$318k=3-6$$

Subtract 6 from 3 to get -3.

$$318k=-3$$

Divide both sides by 318.

$$k=\frac{-3}{318}$$

Reduce the fraction \frac{-3}{318} to lowest terms by extracting and canceling out 3.

$$k=-\frac{1}{106}$$

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

$$307\left(-\frac{1}{106}\right)+b=5$$

Multiply 307 and -\frac{1}{106} to get -\frac{307}{106}.

$$-\frac{307}{106}+b=5$$

Add \frac{307}{106} to both sides.

$$b=5+\frac{307}{106}$$

Add 5 and \frac{307}{106} to get \frac{837}{106}.

$$b=\frac{837}{106}$$

The system is now solved.

$$k=-\frac{1}{106} b=\frac{837}{106}$$