Solve for x (complex solution)
\left\{\begin{matrix}\\x=-1\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&y=1\end{matrix}\right.
Solve for y (complex solution)
\left\{\begin{matrix}\\y=1\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&x=-1\end{matrix}\right.
Solve for x
\left\{\begin{matrix}\\x=-1\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&y=1\end{matrix}\right.
Solve for y
\left\{\begin{matrix}\\y=1\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=-1\end{matrix}\right.
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x-xy+1=y
Swap sides so that all variable terms are on the left hand side.
x-xy=y-1
Subtract 1 from both sides.
\left(1-y\right)x=y-1
Combine all terms containing x.
\frac{\left(1-y\right)x}{1-y}=\frac{y-1}{1-y}
Divide both sides by 1-y.
x=\frac{y-1}{1-y}
Dividing by 1-y undoes the multiplication by 1-y.
x=-1
Divide y-1 by 1-y.
y+xy=x+1
Add xy to both sides.
\left(1+x\right)y=x+1
Combine all terms containing y.
\left(x+1\right)y=x+1
The equation is in standard form.
\frac{\left(x+1\right)y}{x+1}=\frac{x+1}{x+1}
Divide both sides by 1+x.
y=\frac{x+1}{x+1}
Dividing by 1+x undoes the multiplication by 1+x.
y=1
Divide 1+x by 1+x.
x-xy+1=y
Swap sides so that all variable terms are on the left hand side.
x-xy=y-1
Subtract 1 from both sides.
\left(1-y\right)x=y-1
Combine all terms containing x.
\frac{\left(1-y\right)x}{1-y}=\frac{y-1}{1-y}
Divide both sides by 1-y.
x=\frac{y-1}{1-y}
Dividing by 1-y undoes the multiplication by 1-y.
x=-1
Divide y-1 by 1-y.
y+xy=x+1
Add xy to both sides.
\left(1+x\right)y=x+1
Combine all terms containing y.
\left(x+1\right)y=x+1
The equation is in standard form.
\frac{\left(x+1\right)y}{x+1}=\frac{x+1}{x+1}
Divide both sides by 1+x.
y=\frac{x+1}{x+1}
Dividing by 1+x undoes the multiplication by 1+x.
y=1
Divide 1+x by 1+x.
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}