Solve {l}{θ+7d=11}{9+14d=21}

$$\left. \begin{array} { l } { \theta + 7 d = 11 } \\ { 9 + 14 d = 21 } \end{array} \right.$$

Solve for θ, d

$$\theta =5$$

$$d=\frac{6}{7}\approx 0.857142857$$

Solution Steps

Consider the second equation. Subtract 9 from both sides.

$$14d=21-9$$

Subtract 9 from 21 to get 12.

$$14d=12$$

Divide both sides by 14.

$$d=\frac{12}{14}$$

Reduce the fraction \frac{12}{14} to lowest terms by extracting and canceling out 2.

$$d=\frac{6}{7}$$

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

$$\theta +7\times \frac{6}{7}=11$$

Multiply 7 and \frac{6}{7} to get 6.

$$\theta +6=11$$

Subtract 6 from both sides.

$$\theta =11-6$$

Subtract 6 from 11 to get 5.

$$\theta =5$$

The system is now solved.

$$\theta =5 d=\frac{6}{7}$$