Solve {l}{3k+b=2}{3k+2=1}

$$\left. \begin{array} { l } { 3 k + b = 2 } \\ { 3 k + 2 = 1 } \end{array} \right.$$

Solve for k, b

$$k=-\frac{1}{3}\approx -0.333333333$$

$$b=3$$

Solution Steps

Consider the second equation. Subtract 2 from both sides.

$$3k=1-2$$

Subtract 2 from 1 to get -1.

$$3k=-1$$

Divide both sides by 3.

$$k=-\frac{1}{3}$$

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

$$3\left(-\frac{1}{3}\right)+b=2$$

Multiply 3 and -\frac{1}{3} to get -1.

$$-1+b=2$$

Add 1 to both sides.

$$b=2+1$$

Add 2 and 1 to get 3.

$$b=3$$

The system is now solved.

$$k=-\frac{1}{3} b=3$$