Solve {l}{-13/4=b}{-2=1/2k+b}

$$\left\{ \begin{array} { l } { - 1 \frac { 3 } { 4 } = b } \\ { - 2 = \frac { 1 } { 2 } k + b } \end{array} \right.$$

Solve for b, k

$$b = -\frac{7}{4} = -1\frac{3}{4} = -1.75$$

$$k=-\frac{1}{2}=-0.5$$

Solution Steps

Consider the first equation. Multiply 1 and 4 to get 4.

$$-\frac{4+3}{4}=b$$

Add 4 and 3 to get 7.

$$-\frac{7}{4}=b$$

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

$$b=-\frac{7}{4}$$

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

$$-2=\frac{1}{2}k-\frac{7}{4}$$

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

$$\frac{1}{2}k-\frac{7}{4}=-2$$

Add \frac{7}{4} to both sides.

$$\frac{1}{2}k=-2+\frac{7}{4}$$

Add -2 and \frac{7}{4} to get -\frac{1}{4}.

$$\frac{1}{2}k=-\frac{1}{4}$$

Multiply both sides by 2, the reciprocal of \frac{1}{2}.

$$k=-\frac{1}{4}\times 2$$

Multiply -\frac{1}{4} and 2 to get -\frac{1}{2}.

$$k=-\frac{1}{2}$$

The system is now solved.

$$b=-\frac{7}{4} k=-\frac{1}{2}$$