Solve a=frac{uf-v_{1}}{z_{t}}

$$a = \frac { u f - v _ { 1 } } { z _ { t } }$$

Solve for f

$$\left\{\begin{matrix}f=\frac{az_{t}+v_{1}}{u}\text{, }&u\neq 0\text{ and }z_{t}\neq 0\\f\in \mathrm{R}\text{, }&v_{1}=-az_{t}\text{ and }u=0\text{ and }z_{t}\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by z_{t}.

$$az_{t}=uf-v_{1}$$

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

$$uf-v_{1}=az_{t}$$

Add v_{1} to both sides.

$$uf=az_{t}+v_{1}$$

Divide both sides by u.

$$\frac{uf}{u}=\frac{az_{t}+v_{1}}{u}$$

Dividing by u undoes the multiplication by u.

$$f=\frac{az_{t}+v_{1}}{u}$$

Solve for a

$$a=-\frac{v_{1}-fu}{z_{t}}$$

$$z_{t}\neq 0$$