Solve ya_{n}=3n-3?

$$y a _ { n } = 3 n - 3 ?$$

Solve for a_n (complex solution)

$$\left\{\begin{matrix}a_{n}=-\frac{3\left(1-n\right)}{y}\text{, }&y\neq 0\\a_{n}\in \mathrm{C}\text{, }&n=1\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$ya_{n}=3n-3$$

Divide both sides by y.

$$\frac{ya_{n}}{y}=\frac{3n-3}{y}$$

Dividing by y undoes the multiplication by y.

$$a_{n}=\frac{3n-3}{y}$$

Divide -3+3n by y.

$$a_{n}=\frac{3\left(n-1\right)}{y}$$

Solve for a_n

$$\left\{\begin{matrix}a_{n}=-\frac{3\left(1-n\right)}{y}\text{, }&y\neq 0\\a_{n}\in \mathrm{R}\text{, }&n=1\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$ya_{n}=3n-3$$

Divide both sides by y.

$$\frac{ya_{n}}{y}=\frac{3n-3}{y}$$

Dividing by y undoes the multiplication by y.

$$a_{n}=\frac{3n-3}{y}$$

Divide -3+3n by y.

$$a_{n}=\frac{3\left(n-1\right)}{y}$$

Solve for n

$$n=\frac{a_{n}y+3}{3}$$

Steps for Solving Linear Equation

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

$$3n-3=ya_{n}$$

Add 3 to both sides.

$$3n=ya_{n}+3$$

The equation is in standard form.

$$3n=a_{n}y+3$$

Divide both sides by 3.

$$\frac{3n}{3}=\frac{a_{n}y+3}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$n=\frac{a_{n}y+3}{3}$$

Divide ya_{n}+3 by 3.

$$n=\frac{a_{n}y}{3}+1$$