Solve for b (complex solution)
\left\{\begin{matrix}b=-\frac{cy-a}{x-1}\text{, }&x\neq 1\\b\in \mathrm{C}\text{, }&a=cy\text{ and }x=1\end{matrix}\right.
Solve for b
\left\{\begin{matrix}b=-\frac{cy-a}{x-1}\text{, }&x\neq 1\\b\in \mathrm{R}\text{, }&a=cy\text{ and }x=1\end{matrix}\right.
Solve for a
a=bx+cy-b
Graph
Share
Copied to clipboard
bx+cy-b=a
Subtract b from both sides.
bx-b=a-cy
Subtract cy from both sides.
\left(x-1\right)b=a-cy
Combine all terms containing b.
\frac{\left(x-1\right)b}{x-1}=\frac{a-cy}{x-1}
Divide both sides by x-1.
b=\frac{a-cy}{x-1}
Dividing by x-1 undoes the multiplication by x-1.
bx+cy-b=a
Subtract b from both sides.
bx-b=a-cy
Subtract cy from both sides.
\left(x-1\right)b=a-cy
Combine all terms containing b.
\frac{\left(x-1\right)b}{x-1}=\frac{a-cy}{x-1}
Divide both sides by x-1.
b=\frac{a-cy}{x-1}
Dividing by x-1 undoes the multiplication by x-1.
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}