Solve for x
x=\frac{5y}{2y-3}
y\neq \frac{3}{2}
Solve for y
y=\frac{3x}{2x-5}
x\neq \frac{5}{2}
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2xy-3x=5y
Subtract 3x from both sides.
\left(2y-3\right)x=5y
Combine all terms containing x.
\frac{\left(2y-3\right)x}{2y-3}=\frac{5y}{2y-3}
Divide both sides by 2y-3.
x=\frac{5y}{2y-3}
Dividing by 2y-3 undoes the multiplication by 2y-3.
2xy-5y=3x
Subtract 5y from both sides.
\left(2x-5\right)y=3x
Combine all terms containing y.
\frac{\left(2x-5\right)y}{2x-5}=\frac{3x}{2x-5}
Divide both sides by 2x-5.
y=\frac{3x}{2x-5}
Dividing by 2x-5 undoes the multiplication by 2x-5.
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}