Solve y=apx+bp3

$$y = a p x + b p 3$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{bp_{3}-y}{px}\text{, }&x\neq 0\text{ and }p\neq 0\\a\in \mathrm{C}\text{, }&y=bp_{3}\text{ and }\left(x=0\text{ or }p=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$apx+bp_{3}=y$$

Subtract bp_{3} from both sides.

$$apx=y-bp_{3}$$

The equation is in standard form.

$$pxa=y-bp_{3}$$

Divide both sides by px.

$$\frac{pxa}{px}=\frac{y-bp_{3}}{px}$$

Dividing by px undoes the multiplication by px.

$$a=\frac{y-bp_{3}}{px}$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=-\frac{apx-y}{p_{3}}\text{, }&p_{3}\neq 0\\b\in \mathrm{C}\text{, }&y=apx\text{ and }p_{3}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$apx+bp_{3}=y$$

Subtract apx from both sides.

$$bp_{3}=y-apx$$

Reorder the terms.

$$bp_{3}=-apx+y$$

The equation is in standard form.

$$p_{3}b=y-apx$$

Divide both sides by p_{3}.

$$\frac{p_{3}b}{p_{3}}=\frac{y-apx}{p_{3}}$$

Dividing by p_{3} undoes the multiplication by p_{3}.

$$b=\frac{y-apx}{p_{3}}$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{bp_{3}-y}{px}\text{, }&x\neq 0\text{ and }p\neq 0\\a\in \mathrm{R}\text{, }&y=bp_{3}\text{ and }\left(x=0\text{ or }p=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$apx+bp_{3}=y$$

Subtract bp_{3} from both sides.

$$apx=y-bp_{3}$$

The equation is in standard form.

$$pxa=y-bp_{3}$$

Divide both sides by px.

$$\frac{pxa}{px}=\frac{y-bp_{3}}{px}$$

Dividing by px undoes the multiplication by px.

$$a=\frac{y-bp_{3}}{px}$$

Solve for b

$$\left\{\begin{matrix}b=-\frac{apx-y}{p_{3}}\text{, }&p_{3}\neq 0\\b\in \mathrm{R}\text{, }&y=apx\text{ and }p_{3}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$apx+bp_{3}=y$$

Subtract apx from both sides.

$$bp_{3}=y-apx$$

Reorder the terms.

$$bp_{3}=-apx+y$$

The equation is in standard form.

$$p_{3}b=y-apx$$

Divide both sides by p_{3}.

$$\frac{p_{3}b}{p_{3}}=\frac{y-apx}{p_{3}}$$

Dividing by p_{3} undoes the multiplication by p_{3}.

$$b=\frac{y-apx}{p_{3}}$$