Solve for x
x=\frac{2-y}{y+1}
y\neq -1
Solve for y
y=\frac{2-x}{x+1}
x\neq -1
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\left(3x-3\right)\left(y-1\right)=\left(2x-1\right)\left(2y-1\right)
Use the distributive property to multiply 3 by x-1.
3xy-3x-3y+3=\left(2x-1\right)\left(2y-1\right)
Use the distributive property to multiply 3x-3 by y-1.
3xy-3x-3y+3=4xy-2x-2y+1
Use the distributive property to multiply 2x-1 by 2y-1.
3xy-3x-3y+3-4xy=-2x-2y+1
Subtract 4xy from both sides.
-xy-3x-3y+3=-2x-2y+1
Combine 3xy and -4xy to get -xy.
-xy-3x-3y+3+2x=-2y+1
Add 2x to both sides.
-xy-x-3y+3=-2y+1
Combine -3x and 2x to get -x.
-xy-x+3=-2y+1+3y
Add 3y to both sides.
-xy-x+3=y+1
Combine -2y and 3y to get y.
-xy-x=y+1-3
Subtract 3 from both sides.
-xy-x=y-2
Subtract 3 from 1 to get -2.
\left(-y-1\right)x=y-2
Combine all terms containing x.
\frac{\left(-y-1\right)x}{-y-1}=\frac{y-2}{-y-1}
Divide both sides by -y-1.
x=\frac{y-2}{-y-1}
Dividing by -y-1 undoes the multiplication by -y-1.
x=-\frac{y-2}{y+1}
Divide y-2 by -y-1.
\left(3x-3\right)\left(y-1\right)=\left(2x-1\right)\left(2y-1\right)
Use the distributive property to multiply 3 by x-1.
3xy-3x-3y+3=\left(2x-1\right)\left(2y-1\right)
Use the distributive property to multiply 3x-3 by y-1.
3xy-3x-3y+3=4xy-2x-2y+1
Use the distributive property to multiply 2x-1 by 2y-1.
3xy-3x-3y+3-4xy=-2x-2y+1
Subtract 4xy from both sides.
-xy-3x-3y+3=-2x-2y+1
Combine 3xy and -4xy to get -xy.
-xy-3x-3y+3+2y=-2x+1
Add 2y to both sides.
-xy-3x-y+3=-2x+1
Combine -3y and 2y to get -y.
-xy-y+3=-2x+1+3x
Add 3x to both sides.
-xy-y+3=x+1
Combine -2x and 3x to get x.
-xy-y=x+1-3
Subtract 3 from both sides.
-xy-y=x-2
Subtract 3 from 1 to get -2.
\left(-x-1\right)y=x-2
Combine all terms containing y.
\frac{\left(-x-1\right)y}{-x-1}=\frac{x-2}{-x-1}
Divide both sides by -x-1.
y=\frac{x-2}{-x-1}
Dividing by -x-1 undoes the multiplication by -x-1.
y=-\frac{x-2}{x+1}
Divide x-2 by -x-1.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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}