Solve 9a+n(9-1)/2d=-18

$$9a+ \frac{ n(9-1) }{ 2 } d = -18$$

Solve for a

$$a=-\frac{4dn}{9}-2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$18a+n\left(9-1\right)d=-36$$

Subtract 1 from 9 to get 8.

$$18a+n\times 8d=-36$$

Subtract n\times 8d from both sides.

$$18a=-36-n\times 8d$$

Multiply -1 and 8 to get -8.

$$18a=-36-8nd$$

The equation is in standard form.

$$18a=-8dn-36$$

Divide both sides by 18.

$$\frac{18a}{18}=\frac{-8dn-36}{18}$$

Dividing by 18 undoes the multiplication by 18.

$$a=\frac{-8dn-36}{18}$$

Divide -36-8nd by 18.

$$a=-\frac{4dn}{9}-2$$

Solve for d

$$\left\{\begin{matrix}d=-\frac{9\left(a+2\right)}{4n}\text{, }&n\neq 0\\d\in \mathrm{R}\text{, }&a=-2\text{ and }n=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$18a+n\left(9-1\right)d=-36$$

Subtract 1 from 9 to get 8.

$$18a+n\times 8d=-36$$

Subtract 18a from both sides.

$$n\times 8d=-36-18a$$

The equation is in standard form.

$$8nd=-18a-36$$

Divide both sides by 8n.

$$\frac{8nd}{8n}=\frac{-18a-36}{8n}$$

Dividing by 8n undoes the multiplication by 8n.

$$d=\frac{-18a-36}{8n}$$

Divide -36-18a by 8n.

$$d=-\frac{9\left(a+2\right)}{4n}$$