Solve {l}{3/7A+3/6=15}{3/4A-B=2}

$$\left. \begin{array} { l } { \frac { 3 } { 7 } A + \frac { 3 } { 6 } = 15 } \\ { \frac { 3 } { 4 } A - B = 2 } \end{array} \right.$$

Solve for A, B

$$A = \frac{203}{6} = 33\frac{5}{6} \approx 33.833333333$$

$$B = \frac{187}{8} = 23\frac{3}{8} = 23.375$$

Solution Steps

Consider the first equation. Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{3}{7}A+\frac{1}{2}=15$$

Subtract \frac{1}{2} from both sides.

$$\frac{3}{7}A=15-\frac{1}{2}$$

Subtract \frac{1}{2} from 15 to get \frac{29}{2}.

$$\frac{3}{7}A=\frac{29}{2}$$

Multiply both sides by \frac{7}{3}, the reciprocal of \frac{3}{7}.

$$A=\frac{29}{2}\times \frac{7}{3}$$

Multiply \frac{29}{2} and \frac{7}{3} to get \frac{203}{6}.

$$A=\frac{203}{6}$$

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

$$\frac{3}{4}\times \frac{203}{6}-B=2$$

Multiply \frac{3}{4} and \frac{203}{6} to get \frac{203}{8}.

$$\frac{203}{8}-B=2$$

Subtract \frac{203}{8} from both sides.

$$-B=2-\frac{203}{8}$$

Subtract \frac{203}{8} from 2 to get -\frac{187}{8}.

$$-B=-\frac{187}{8}$$

Divide both sides by -1.

$$B=\frac{-\frac{187}{8}}{-1}$$

Express \frac{-\frac{187}{8}}{-1} as a single fraction.

$$B=\frac{-187}{8\left(-1\right)}$$

Multiply 8 and -1 to get -8.

$$B=\frac{-187}{-8}$$

Fraction \frac{-187}{-8} can be simplified to \frac{187}{8} by removing the negative sign from both the numerator and the denominator.

$$B=\frac{187}{8}$$

The system is now solved.

$$A=\frac{203}{6} B=\frac{187}{8}$$