Solve for x (complex solution)
\left\{\begin{matrix}x=-\frac{\alpha -y}{\beta }\text{, }&\beta \neq 0\\x\in \mathrm{C}\text{, }&y=\alpha \text{ and }\beta =0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=-\frac{\alpha -y}{\beta }\text{, }&\beta \neq 0\\x\in \mathrm{R}\text{, }&y=\alpha \text{ and }\beta =0\end{matrix}\right.
Solve for y
y=x\beta +\alpha
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\beta x+\alpha =y
Swap sides so that all variable terms are on the left hand side.
\beta x=y-\alpha
Subtract \alpha from both sides.
\frac{\beta x}{\beta }=\frac{y-\alpha }{\beta }
Divide both sides by \beta .
x=\frac{y-\alpha }{\beta }
Dividing by \beta undoes the multiplication by \beta .
\beta x+\alpha =y
Swap sides so that all variable terms are on the left hand side.
\beta x=y-\alpha
Subtract \alpha from both sides.
\frac{\beta x}{\beta }=\frac{y-\alpha }{\beta }
Divide both sides by \beta .
x=\frac{y-\alpha }{\beta }
Dividing by \beta undoes the multiplication by \beta .
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