Solve for x
x=-\frac{1}{4\left(1-2y\right)}
y\neq \frac{1}{2}
Solve for y
y=\frac{1}{2}+\frac{1}{8x}
x\neq 0
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-8xy+4x=-1
Subtract 1 from both sides. Anything subtracted from zero gives its negation.
\left(-8y+4\right)x=-1
Combine all terms containing x.
\left(4-8y\right)x=-1
The equation is in standard form.
\frac{\left(4-8y\right)x}{4-8y}=-\frac{1}{4-8y}
Divide both sides by -8y+4.
x=-\frac{1}{4-8y}
Dividing by -8y+4 undoes the multiplication by -8y+4.
x=-\frac{1}{4\left(1-2y\right)}
Divide -1 by -8y+4.
-8xy+1=-4x
Subtract 4x from both sides. Anything subtracted from zero gives its negation.
-8xy=-4x-1
Subtract 1 from both sides.
\left(-8x\right)y=-4x-1
The equation is in standard form.
\frac{\left(-8x\right)y}{-8x}=\frac{-4x-1}{-8x}
Divide both sides by -8x.
y=\frac{-4x-1}{-8x}
Dividing by -8x undoes the multiplication by -8x.
y=\frac{1}{2}+\frac{1}{8x}
Divide -4x-1 by -8x.
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}