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.
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.
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.
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.
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apx+bp_{3}=y
Swap sides so that all variable terms are on the left hand side.
apx=y-bp_{3}
Subtract bp_{3} from both sides.
pxa=y-bp_{3}
The equation is in standard form.
\frac{pxa}{px}=\frac{y-bp_{3}}{px}
Divide both sides by px.
a=\frac{y-bp_{3}}{px}
Dividing by px undoes the multiplication by px.
apx+bp_{3}=y
Swap sides so that all variable terms are on the left hand side.
bp_{3}=y-apx
Subtract apx from both sides.
bp_{3}=-apx+y
Reorder the terms.
p_{3}b=y-apx
The equation is in standard form.
\frac{p_{3}b}{p_{3}}=\frac{y-apx}{p_{3}}
Divide both sides by p_{3}.
b=\frac{y-apx}{p_{3}}
Dividing by p_{3} undoes the multiplication by p_{3}.
apx+bp_{3}=y
Swap sides so that all variable terms are on the left hand side.
apx=y-bp_{3}
Subtract bp_{3} from both sides.
pxa=y-bp_{3}
The equation is in standard form.
\frac{pxa}{px}=\frac{y-bp_{3}}{px}
Divide both sides by px.
a=\frac{y-bp_{3}}{px}
Dividing by px undoes the multiplication by px.
apx+bp_{3}=y
Swap sides so that all variable terms are on the left hand side.
bp_{3}=y-apx
Subtract apx from both sides.
bp_{3}=-apx+y
Reorder the terms.
p_{3}b=y-apx
The equation is in standard form.
\frac{p_{3}b}{p_{3}}=\frac{y-apx}{p_{3}}
Divide both sides by p_{3}.
b=\frac{y-apx}{p_{3}}
Dividing by p_{3} undoes the multiplication by p_{3}.
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