Solve {l}{a_{1}+2d=7}{a_{1}+4d=a_{1}+d+6}

$$\left. \begin{array} { l } { a _ { 1 } + 2 d = 7 } \\ { a _ { 1 } + 4 d = a _ { 1 } + d + 6 } \end{array} \right.$$

Solve for a_1, d

$$a_{1}=3$$

$$d=2$$

Solution Steps

Consider the second equation. Subtract a_{1} from both sides.

$$a_{1}+4d-a_{1}=d+6$$

Combine a_{1} and -a_{1} to get 0.

$$4d=d+6$$

Subtract d from both sides.

$$4d-d=6$$

Combine 4d and -d to get 3d.

$$3d=6$$

Divide both sides by 3.

$$d=\frac{6}{3}$$

Divide 6 by 3 to get 2.

$$d=2$$

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

$$a_{1}+2\times 2=7$$

Multiply 2 and 2 to get 4.

$$a_{1}+4=7$$

Subtract 4 from both sides.

$$a_{1}=7-4$$

Subtract 4 from 7 to get 3.

$$a_{1}=3$$

The system is now solved.

$$a_{1}=3 d=2$$