Solve {l}{-9/4=12+b}{1=4k+b}

$$\left\{ \begin{array} { l } { - \frac { 9 } { 4 } = 12 + b } \\ { 1 = 4 k + b } \end{array} \right.$$

Solve for b, k

$$b = -\frac{57}{4} = -14\frac{1}{4} = -14.25$$

$$k = \frac{61}{16} = 3\frac{13}{16} = 3.8125$$

Solution Steps

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

$$12+b=-\frac{9}{4}$$

Subtract 12 from both sides.

$$b=-\frac{9}{4}-12$$

Subtract 12 from -\frac{9}{4} to get -\frac{57}{4}.

$$b=-\frac{57}{4}$$

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

$$1=4k-\frac{57}{4}$$

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

$$4k-\frac{57}{4}=1$$

Add \frac{57}{4} to both sides.

$$4k=1+\frac{57}{4}$$

Add 1 and \frac{57}{4} to get \frac{61}{4}.

$$4k=\frac{61}{4}$$

Divide both sides by 4.

$$k=\frac{\frac{61}{4}}{4}$$

Express \frac{\frac{61}{4}}{4} as a single fraction.

$$k=\frac{61}{4\times 4}$$

Multiply 4 and 4 to get 16.

$$k=\frac{61}{16}$$

The system is now solved.

$$b=-\frac{57}{4} k=\frac{61}{16}$$