Solve {l}{b+a=3}{2b+1/2=5}

$$\left\{ \begin{array} { l } { b + a = 3 } \\ { \frac { 2 b + 1 } { 2 } = 5 } \end{array} \right.$$

Solve for b, a

$$b = \frac{9}{2} = 4\frac{1}{2} = 4.5$$

$$a = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

Solution Steps

Consider the second equation. Multiply both sides by 2.

$$2b+1=5\times 2$$

Multiply 5 and 2 to get 10.

$$2b+1=10$$

Subtract 1 from both sides.

$$2b=10-1$$

Subtract 1 from 10 to get 9.

$$2b=9$$

Divide both sides by 2.

$$b=\frac{9}{2}$$

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

$$\frac{9}{2}+a=3$$

Subtract \frac{9}{2} from both sides.

$$a=3-\frac{9}{2}$$

Subtract \frac{9}{2} from 3 to get -\frac{3}{2}.

$$a=-\frac{3}{2}$$

The system is now solved.

$$b=\frac{9}{2} a=-\frac{3}{2}$$