Solve for x
x=-\frac{1}{2y-5}
y\neq \frac{5}{2}
Solve for y
y=\frac{5}{2}-\frac{1}{2x}
x\neq 0
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2yx=x\times 5-1
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.
2yx-x\times 5=-1
Subtract x\times 5 from both sides.
2yx-5x=-1
Multiply -1 and 5 to get -5.
\left(2y-5\right)x=-1
Combine all terms containing x.
\frac{\left(2y-5\right)x}{2y-5}=-\frac{1}{2y-5}
Divide both sides by 2y-5.
x=-\frac{1}{2y-5}
Dividing by 2y-5 undoes the multiplication by 2y-5.
x=-\frac{1}{2y-5}\text{, }x\neq 0
Variable x cannot be equal to 0.
2yx=x\times 5-1
Multiply both sides of the equation by x.
2xy=5x-1
The equation is in standard form.
\frac{2xy}{2x}=\frac{5x-1}{2x}
Divide both sides by 2x.
y=\frac{5x-1}{2x}
Dividing by 2x undoes the multiplication by 2x.
y=\frac{5}{2}-\frac{1}{2x}
Divide 5x-1 by 2x.
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}