Solve for A (complex solution)
\left\{\begin{matrix}A=\frac{CE}{F}\text{, }&D\neq 0\text{ and }E\neq 0\text{ and }F\neq 0\\A\in \mathrm{C}\text{, }&B=0\text{ and }F\neq 0\text{ and }D\neq 0\text{ and }E\neq 0\end{matrix}\right.
Solve for B (complex solution)
\left\{\begin{matrix}B=0\text{, }&D\neq 0\text{ and }E\neq 0\text{ and }F\neq 0\\B\in \mathrm{C}\text{, }&\left(E\neq 0\text{ and }A=0\text{ and }C=0\text{ and }D\neq 0\text{ and }F\neq 0\right)\text{ or }\left(E=\frac{AF}{C}\text{ and }F\neq 0\text{ and }A\neq 0\text{ and }C\neq 0\text{ and }D\neq 0\right)\end{matrix}\right.
Solve for A
\left\{\begin{matrix}A=\frac{CE}{F}\text{, }&D\neq 0\text{ and }E\neq 0\text{ and }F\neq 0\\A\in \mathrm{R}\text{, }&B=0\text{ and }F\neq 0\text{ and }D\neq 0\text{ and }E\neq 0\end{matrix}\right.
Solve for B
\left\{\begin{matrix}B=0\text{, }&D\neq 0\text{ and }E\neq 0\text{ and }F\neq 0\\B\in \mathrm{R}\text{, }&\left(E\neq 0\text{ and }A=0\text{ and }C=0\text{ and }D\neq 0\text{ and }F\neq 0\right)\text{ or }\left(E=\frac{AF}{C}\text{ and }F\neq 0\text{ and }A\neq 0\text{ and }C\neq 0\text{ and }D\neq 0\right)\end{matrix}\right.
Share
Copied to clipboard
FAB=EBC
Multiply both sides of the equation by DEF, the least common multiple of DE,DF.
ABF=BCE
Reorder the terms.
BFA=BCE
The equation is in standard form.
\frac{BFA}{BF}=\frac{BCE}{BF}
Divide both sides by BF.
A=\frac{BCE}{BF}
Dividing by BF undoes the multiplication by BF.
A=\frac{CE}{F}
Divide BCE by BF.
FAB=EBC
Multiply both sides of the equation by DEF, the least common multiple of DE,DF.
FAB-EBC=0
Subtract EBC from both sides.
ABF-BCE=0
Reorder the terms.
\left(AF-CE\right)B=0
Combine all terms containing B.
B=0
Divide 0 by AF-CE.
FAB=EBC
Multiply both sides of the equation by DEF, the least common multiple of DE,DF.
ABF=BCE
Reorder the terms.
BFA=BCE
The equation is in standard form.
\frac{BFA}{BF}=\frac{BCE}{BF}
Divide both sides by BF.
A=\frac{BCE}{BF}
Dividing by BF undoes the multiplication by BF.
A=\frac{CE}{F}
Divide BCE by BF.
FAB=EBC
Multiply both sides of the equation by DEF, the least common multiple of DE,DF.
FAB-EBC=0
Subtract EBC from both sides.
ABF-BCE=0
Reorder the terms.
\left(AF-CE\right)B=0
Combine all terms containing B.
B=0
Divide 0 by AF-CE.
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}