Solve {l}{(4+B)1/2-B=3/4}{(2A+B)1/4-B=5/4}

$$\left\{ \begin{array} { l } { ( 4 + B ) \frac { 1 } { 2 } - B = \frac { 3 } { 4 } } \\ { ( 2 A + B ) \frac { 1 } { 4 } - B = \frac { 5 } { 4 } } \end{array} \right.$$

Solve for B, A

$$B = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

$$A = \frac{25}{4} = 6\frac{1}{4} = 6.25$$

Solution Steps

Consider the first equation. Use the distributive property to multiply 4+B by \frac{1}{2}.

$$2+\frac{1}{2}B-B=\frac{3}{4}$$

Combine \frac{1}{2}B and -B to get -\frac{1}{2}B.

$$2-\frac{1}{2}B=\frac{3}{4}$$

Subtract 2 from both sides.

$$-\frac{1}{2}B=\frac{3}{4}-2$$

Subtract 2 from \frac{3}{4} to get -\frac{5}{4}.

$$-\frac{1}{2}B=-\frac{5}{4}$$

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

$$B=-\frac{5}{4}\left(-2\right)$$

Multiply -\frac{5}{4} and -2 to get \frac{5}{2}.

$$B=\frac{5}{2}$$

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

$$\left(2A+\frac{5}{2}\right)\times \frac{1}{4}-\frac{5}{2}=\frac{5}{4}$$

Use the distributive property to multiply 2A+\frac{5}{2} by \frac{1}{4}.

$$\frac{1}{2}A+\frac{5}{8}-\frac{5}{2}=\frac{5}{4}$$

Subtract \frac{5}{2} from \frac{5}{8} to get -\frac{15}{8}.

$$\frac{1}{2}A-\frac{15}{8}=\frac{5}{4}$$

Add \frac{15}{8} to both sides.

$$\frac{1}{2}A=\frac{5}{4}+\frac{15}{8}$$

Add \frac{5}{4} and \frac{15}{8} to get \frac{25}{8}.

$$\frac{1}{2}A=\frac{25}{8}$$

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

$$A=\frac{25}{8}\times 2$$

Multiply \frac{25}{8} and 2 to get \frac{25}{4}.

$$A=\frac{25}{4}$$

The system is now solved.

$$B=\frac{5}{2} A=\frac{25}{4}$$