Solve for A
\left\{\begin{matrix}A=\frac{B_{18}+1}{3B}\text{, }&B\neq 0\\A\in \mathrm{R}\text{, }&B_{18}=-1\text{ and }B=0\end{matrix}\right.
Solve for B
\left\{\begin{matrix}B=\frac{B_{18}+1}{3A}\text{, }&A\neq 0\\B\in \mathrm{R}\text{, }&B_{18}=-1\text{ and }A=0\end{matrix}\right.
Share
Copied to clipboard
3AB-1=B_{18}
Combine 2AB and AB to get 3AB.
3AB=B_{18}+1
Add 1 to both sides.
3BA=B_{18}+1
The equation is in standard form.
\frac{3BA}{3B}=\frac{B_{18}+1}{3B}
Divide both sides by 3B.
A=\frac{B_{18}+1}{3B}
Dividing by 3B undoes the multiplication by 3B.
3AB-1=B_{18}
Combine 2AB and AB to get 3AB.
3AB=B_{18}+1
Add 1 to both sides.
\frac{3AB}{3A}=\frac{B_{18}+1}{3A}
Divide both sides by 3A.
B=\frac{B_{18}+1}{3A}
Dividing by 3A undoes the multiplication by 3A.
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}