Solve for a (complex solution)
\left\{\begin{matrix}a=-\frac{bx}{2b-y}\text{, }&b\neq \frac{y}{2}\\a\in \mathrm{C}\text{, }&\left(b=0\text{ and }y=0\right)\text{ or }\left(x=0\text{ and }b=\frac{y}{2}\right)\end{matrix}\right.
Solve for b (complex solution)
\left\{\begin{matrix}b=\frac{ay}{x+2a}\text{, }&x\neq -2a\\b\in \mathrm{C}\text{, }&\left(a=0\text{ and }x=0\right)\text{ or }\left(y=0\text{ and }x=-2a\right)\end{matrix}\right.
Solve for a
\left\{\begin{matrix}a=-\frac{bx}{2b-y}\text{, }&b\neq \frac{y}{2}\\a\in \mathrm{R}\text{, }&\left(b=0\text{ and }y=0\right)\text{ or }\left(x=0\text{ and }b=\frac{y}{2}\right)\end{matrix}\right.
Solve for b
\left\{\begin{matrix}b=\frac{ay}{x+2a}\text{, }&x\neq -2a\\b\in \mathrm{R}\text{, }&\left(a=0\text{ and }x=0\right)\text{ or }\left(y=0\text{ and }x=-2a\right)\end{matrix}\right.
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-ay+2ab=-bx
Subtract bx from both sides. Anything subtracted from zero gives its negation.
\left(-y+2b\right)a=-bx
Combine all terms containing a.
\left(2b-y\right)a=-bx
The equation is in standard form.
\frac{\left(2b-y\right)a}{2b-y}=-\frac{bx}{2b-y}
Divide both sides by -y+2b.
a=-\frac{bx}{2b-y}
Dividing by -y+2b undoes the multiplication by -y+2b.
bx+2ab=ay
Add ay to both sides. Anything plus zero gives itself.
\left(x+2a\right)b=ay
Combine all terms containing b.
\frac{\left(x+2a\right)b}{x+2a}=\frac{ay}{x+2a}
Divide both sides by x+2a.
b=\frac{ay}{x+2a}
Dividing by x+2a undoes the multiplication by x+2a.
-ay+2ab=-bx
Subtract bx from both sides. Anything subtracted from zero gives its negation.
\left(-y+2b\right)a=-bx
Combine all terms containing a.
\left(2b-y\right)a=-bx
The equation is in standard form.
\frac{\left(2b-y\right)a}{2b-y}=-\frac{bx}{2b-y}
Divide both sides by -y+2b.
a=-\frac{bx}{2b-y}
Dividing by -y+2b undoes the multiplication by -y+2b.
bx+2ab=ay
Add ay to both sides. Anything plus zero gives itself.
\left(x+2a\right)b=ay
Combine all terms containing b.
\frac{\left(x+2a\right)b}{x+2a}=\frac{ay}{x+2a}
Divide both sides by x+2a.
b=\frac{ay}{x+2a}
Dividing by x+2a undoes the multiplication by x+2a.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
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}