Solve for a
\left\{\begin{matrix}a=\frac{y-x}{b}\text{, }&y\neq x\text{ and }b\neq 0\\a\neq 0\text{, }&b=0\text{ and }y=x\end{matrix}\right.
Solve for b
b=\frac{y-x}{a}
a\neq 0
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y-x=ba
Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by a.
ba=y-x
Swap sides so that all variable terms are on the left hand side.
\frac{ba}{b}=\frac{y-x}{b}
Divide both sides by b.
a=\frac{y-x}{b}
Dividing by b undoes the multiplication by b.
a=\frac{y-x}{b}\text{, }a\neq 0
Variable a cannot be equal to 0.
y-x=ba
Multiply both sides of the equation by a.
ba=y-x
Swap sides so that all variable terms are on the left hand side.
ab=y-x
The equation is in standard form.
\frac{ab}{a}=\frac{y-x}{a}
Divide both sides by a.
b=\frac{y-x}{a}
Dividing by a undoes the multiplication by a.
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Limits
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