Solve eta=frac{N_{1}-N_{2}}{N_{1}}

$$\eta = \frac { N _ { 1 } - N _ { 2 } } { N _ { 1 } }$$

Solve for N_1

$$\left\{\begin{matrix}N_{1}=-\frac{N_{2}}{\eta -1}\text{, }&N_{2}\neq 0\text{ and }\eta \neq 1\\N_{1}\neq 0\text{, }&N_{2}=0\text{ and }\eta =1\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable N_{1} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by N_{1}.

$$\eta N_{1}=N_{1}-N_{2}$$

Subtract N_{1} from both sides.

$$\eta N_{1}-N_{1}=-N_{2}$$

Combine all terms containing N_{1}.

$$\left(\eta -1\right)N_{1}=-N_{2}$$

Divide both sides by \eta -1.

$$\frac{\left(\eta -1\right)N_{1}}{\eta -1}=-\frac{N_{2}}{\eta -1}$$

Dividing by \eta -1 undoes the multiplication by \eta -1.

$$N_{1}=-\frac{N_{2}}{\eta -1}$$

Variable N_{1} cannot be equal to 0.

$$N_{1}=-\frac{N_{2}}{\eta -1}\text{, }N_{1}\neq 0$$

Solve for N_2

$$N_{2}=N_{1}\left(1-\eta \right)$$

$$N_{1}\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by N_{1}.

$$\eta N_{1}=N_{1}-N_{2}$$

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

$$N_{1}-N_{2}=\eta N_{1}$$

Subtract N_{1} from both sides.

$$-N_{2}=\eta N_{1}-N_{1}$$

The equation is in standard form.

$$-N_{2}=N_{1}\eta -N_{1}$$

Divide both sides by -1.

$$\frac{-N_{2}}{-1}=\frac{N_{1}\left(\eta -1\right)}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$N_{2}=\frac{N_{1}\left(\eta -1\right)}{-1}$$

Divide N_{1}\left(-1+\eta \right) by -1.

$$N_{2}=N_{1}-N_{1}\eta$$