Solve for x
x=\frac{2}{5y+2}
y\neq -\frac{2}{5}
Solve for y
y=-\frac{2}{5}+\frac{2}{5x}
x\neq 0
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2x+5xy=2
Add 2 to both sides. Anything plus zero gives itself.
\left(2+5y\right)x=2
Combine all terms containing x.
\left(5y+2\right)x=2
The equation is in standard form.
\frac{\left(5y+2\right)x}{5y+2}=\frac{2}{5y+2}
Divide both sides by 2+5y.
x=\frac{2}{5y+2}
Dividing by 2+5y undoes the multiplication by 2+5y.
5xy-2=-2x
Subtract 2x from both sides. Anything subtracted from zero gives its negation.
5xy=-2x+2
Add 2 to both sides.
5xy=2-2x
The equation is in standard form.
\frac{5xy}{5x}=\frac{2-2x}{5x}
Divide both sides by 5x.
y=\frac{2-2x}{5x}
Dividing by 5x undoes the multiplication by 5x.
y=-\frac{2}{5}+\frac{2}{5x}
Divide -2x+2 by 5x.
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}