Solve {l}{9-5/3+b=0}{a/4-5/2+b=0}

$$\left\{ \begin{array} { l } { 9 - \frac { 5 } { 3 } + b = 0 } \\ { \frac { a } { 4 } - \frac { 5 } { 2 } + b = 0 } \end{array} \right.$$

Solve for b, a

$$b = -\frac{22}{3} = -7\frac{1}{3} \approx -7.333333333$$

$$a = \frac{118}{3} = 39\frac{1}{3} \approx 39.333333333$$

Solution Steps

Consider the first equation. Subtract \frac{5}{3} from 9 to get \frac{22}{3}.

$$\frac{22}{3}+b=0$$

Subtract \frac{22}{3} from both sides. Anything subtracted from zero gives its negation.

$$b=-\frac{22}{3}$$

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

$$\frac{a}{4}-\frac{5}{2}-\frac{22}{3}=0$$

Multiply both sides of the equation by 12, the least common multiple of 4,2,3.

$$3a-30-88=0$$

Subtract 88 from -30 to get -118.

$$3a-118=0$$

Add 118 to both sides. Anything plus zero gives itself.

$$3a=118$$

Divide both sides by 3.

$$a=\frac{118}{3}$$

The system is now solved.

$$b=-\frac{22}{3} a=\frac{118}{3}$$