Solve for a (complex solution)
\left\{\begin{matrix}a=\frac{x\left(b+m\right)}{y}\text{, }&y\neq 0\\a\in \mathrm{C}\text{, }&\left(x=0\text{ or }m=-b\right)\text{ and }y=0\end{matrix}\right.
Solve for b (complex solution)
\left\{\begin{matrix}b=\frac{ay}{x}-m\text{, }&x\neq 0\\b\in \mathrm{C}\text{, }&\left(a=0\text{ or }y=0\right)\text{ and }x=0\end{matrix}\right.
Solve for a
\left\{\begin{matrix}a=\frac{x\left(b+m\right)}{y}\text{, }&y\neq 0\\a\in \mathrm{R}\text{, }&\left(x=0\text{ or }m=-b\right)\text{ and }y=0\end{matrix}\right.
Solve for b
\left\{\begin{matrix}b=\frac{ay}{x}-m\text{, }&x\neq 0\\b\in \mathrm{R}\text{, }&\left(a=0\text{ or }y=0\right)\text{ and }x=0\end{matrix}\right.
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ay-bx=mx
Swap sides so that all variable terms are on the left hand side.
ay=mx+bx
Add bx to both sides.
ya=bx+mx
The equation is in standard form.
\frac{ya}{y}=\frac{x\left(b+m\right)}{y}
Divide both sides by y.
a=\frac{x\left(b+m\right)}{y}
Dividing by y undoes the multiplication by y.
ay-bx=mx
Swap sides so that all variable terms are on the left hand side.
-bx=mx-ay
Subtract ay from both sides.
\left(-x\right)b=mx-ay
The equation is in standard form.
\frac{\left(-x\right)b}{-x}=\frac{mx-ay}{-x}
Divide both sides by -x.
b=\frac{mx-ay}{-x}
Dividing by -x undoes the multiplication by -x.
b=\frac{ay}{x}-m
Divide mx-ay by -x.
ay-bx=mx
Swap sides so that all variable terms are on the left hand side.
ay=mx+bx
Add bx to both sides.
ya=bx+mx
The equation is in standard form.
\frac{ya}{y}=\frac{x\left(b+m\right)}{y}
Divide both sides by y.
a=\frac{x\left(b+m\right)}{y}
Dividing by y undoes the multiplication by y.
ay-bx=mx
Swap sides so that all variable terms are on the left hand side.
-bx=mx-ay
Subtract ay from both sides.
\left(-x\right)b=mx-ay
The equation is in standard form.
\frac{\left(-x\right)b}{-x}=\frac{mx-ay}{-x}
Divide both sides by -x.
b=\frac{mx-ay}{-x}
Dividing by -x undoes the multiplication by -x.
b=\frac{ay}{x}-m
Divide mx-ay by -x.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}