Solve {l}{8=2a+6d}{16=3a+12a}

$$\left. \begin{array} { l } { 8 = 2 a + 6 d } \\ { 16 = 3 a + 12 a } \end{array} \right.$$

Solve for a, d

$$a = \frac{16}{15} = 1\frac{1}{15} \approx 1.066666667$$

$$d=\frac{44}{45}\approx 0.977777778$$

Solution Steps

Consider the second equation. Combine 3a and 12a to get 15a.

$$16=15a$$

Swap sides so that all variable terms are on the left hand side.

$$15a=16$$

Divide both sides by 15.

$$a=\frac{16}{15}$$

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

$$8=2\times \frac{16}{15}+6d$$

Multiply 2 and \frac{16}{15} to get \frac{32}{15}.

$$8=\frac{32}{15}+6d$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{32}{15}+6d=8$$

Subtract \frac{32}{15} from both sides.

$$6d=8-\frac{32}{15}$$

Subtract \frac{32}{15} from 8 to get \frac{88}{15}.

$$6d=\frac{88}{15}$$

Divide both sides by 6.

$$d=\frac{\frac{88}{15}}{6}$$

Express \frac{\frac{88}{15}}{6} as a single fraction.

$$d=\frac{88}{15\times 6}$$

Multiply 15 and 6 to get 90.

$$d=\frac{88}{90}$$

Reduce the fraction \frac{88}{90} to lowest terms by extracting and canceling out 2.

$$d=\frac{44}{45}$$

The system is now solved.

$$a=\frac{16}{15} d=\frac{44}{45}$$