Solve for k (complex solution)
\left\{\begin{matrix}k=-\frac{12-y}{x-5}\text{, }&x\neq 5\\k\in \mathrm{C}\text{, }&y=12\text{ and }x=5\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}x=\frac{y+5k-12}{k}\text{, }&k\neq 0\\x\in \mathrm{C}\text{, }&y=12\text{ and }k=0\end{matrix}\right.
Solve for k
\left\{\begin{matrix}k=-\frac{12-y}{x-5}\text{, }&x\neq 5\\k\in \mathrm{R}\text{, }&y=12\text{ and }x=5\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=\frac{y+5k-12}{k}\text{, }&k\neq 0\\x\in \mathrm{R}\text{, }&y=12\text{ and }k=0\end{matrix}\right.
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y=kx-5k+12
Use the distributive property to multiply k by x-5.
kx-5k+12=y
Swap sides so that all variable terms are on the left hand side.
kx-5k=y-12
Subtract 12 from both sides.
\left(x-5\right)k=y-12
Combine all terms containing k.
\frac{\left(x-5\right)k}{x-5}=\frac{y-12}{x-5}
Divide both sides by x-5.
k=\frac{y-12}{x-5}
Dividing by x-5 undoes the multiplication by x-5.
y=kx-5k+12
Use the distributive property to multiply k by x-5.
kx-5k+12=y
Swap sides so that all variable terms are on the left hand side.
kx+12=y+5k
Add 5k to both sides.
kx=y+5k-12
Subtract 12 from both sides.
\frac{kx}{k}=\frac{y+5k-12}{k}
Divide both sides by k.
x=\frac{y+5k-12}{k}
Dividing by k undoes the multiplication by k.
y=kx-5k+12
Use the distributive property to multiply k by x-5.
kx-5k+12=y
Swap sides so that all variable terms are on the left hand side.
kx-5k=y-12
Subtract 12 from both sides.
\left(x-5\right)k=y-12
Combine all terms containing k.
\frac{\left(x-5\right)k}{x-5}=\frac{y-12}{x-5}
Divide both sides by x-5.
k=\frac{y-12}{x-5}
Dividing by x-5 undoes the multiplication by x-5.
y=kx-5k+12
Use the distributive property to multiply k by x-5.
kx-5k+12=y
Swap sides so that all variable terms are on the left hand side.
kx+12=y+5k
Add 5k to both sides.
kx=y+5k-12
Subtract 12 from both sides.
\frac{kx}{k}=\frac{y+5k-12}{k}
Divide both sides by k.
x=\frac{y+5k-12}{k}
Dividing by k undoes the multiplication by k.
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}