Solve {l}{7+15B=10}{8A-9B=26}

$$\left. \begin{array} { l } { 7 + 15 B = 10 } \\ { 8 A - 9 B = 26 } \end{array} \right.$$

Solve for B, A

$$B=\frac{1}{5}=0.2$$

$$A = \frac{139}{40} = 3\frac{19}{40} = 3.475$$

Solution Steps

Consider the first equation. Subtract 7 from both sides.

$$15B=10-7$$

Subtract 7 from 10 to get 3.

$$15B=3$$

Divide both sides by 15.

$$B=\frac{3}{15}$$

Reduce the fraction \frac{3}{15} to lowest terms by extracting and canceling out 3.

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

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

$$8A-9\times \frac{1}{5}=26$$

Multiply -9 and \frac{1}{5} to get -\frac{9}{5}.

$$8A-\frac{9}{5}=26$$

Add \frac{9}{5} to both sides.

$$8A=26+\frac{9}{5}$$

Add 26 and \frac{9}{5} to get \frac{139}{5}.

$$8A=\frac{139}{5}$$

Divide both sides by 8.

$$A=\frac{\frac{139}{5}}{8}$$

Express \frac{\frac{139}{5}}{8} as a single fraction.

$$A=\frac{139}{5\times 8}$$

Multiply 5 and 8 to get 40.

$$A=\frac{139}{40}$$

The system is now solved.

$$B=\frac{1}{5} A=\frac{139}{40}$$