Solve {l}{2a+16d=86}{29+28d=132}

$$\left. \begin{array} { l } { 2 a + 16 d = 86 } \\ { 29 + 28 d = 132 } \end{array} \right.$$

Solve for a, d

$$a = \frac{95}{7} = 13\frac{4}{7} \approx 13.571428571$$

$$d = \frac{103}{28} = 3\frac{19}{28} \approx 3.678571429$$

Solution Steps

Consider the second equation. Subtract 29 from both sides.

$$28d=132-29$$

Subtract 29 from 132 to get 103.

$$28d=103$$

Divide both sides by 28.

$$d=\frac{103}{28}$$

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

$$2a+16\times \frac{103}{28}=86$$

Multiply 16 and \frac{103}{28} to get \frac{412}{7}.

$$2a+\frac{412}{7}=86$$

Subtract \frac{412}{7} from both sides.

$$2a=86-\frac{412}{7}$$

Subtract \frac{412}{7} from 86 to get \frac{190}{7}.

$$2a=\frac{190}{7}$$

Divide both sides by 2.

$$a=\frac{\frac{190}{7}}{2}$$

Express \frac{\frac{190}{7}}{2} as a single fraction.

$$a=\frac{190}{7\times 2}$$

Multiply 7 and 2 to get 14.

$$a=\frac{190}{14}$$

Reduce the fraction \frac{190}{14} to lowest terms by extracting and canceling out 2.

$$a=\frac{95}{7}$$

The system is now solved.

$$a=\frac{95}{7} d=\frac{103}{28}$$