Solve for x
x=-\frac{3}{2-3y}
y\neq \frac{2}{3}
Solve for y
y=\frac{2}{3}+\frac{1}{x}
x\neq 0
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4x+6=6xy
Multiply both sides of the equation by 2.
4x+6-6xy=0
Subtract 6xy from both sides.
4x-6xy=-6
Subtract 6 from both sides. Anything subtracted from zero gives its negation.
\left(4-6y\right)x=-6
Combine all terms containing x.
\frac{\left(4-6y\right)x}{4-6y}=-\frac{6}{4-6y}
Divide both sides by 4-6y.
x=-\frac{6}{4-6y}
Dividing by 4-6y undoes the multiplication by 4-6y.
x=-\frac{3}{2-3y}
Divide -6 by 4-6y.
4x+6=6xy
Multiply both sides of the equation by 2.
6xy=4x+6
Swap sides so that all variable terms are on the left hand side.
\frac{6xy}{6x}=\frac{4x+6}{6x}
Divide both sides by 6x.
y=\frac{4x+6}{6x}
Dividing by 6x undoes the multiplication by 6x.
y=\frac{2}{3}+\frac{1}{x}
Divide 4x+6 by 6x.
Examples
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{ 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}