Solve for x
x=-\frac{4}{5y-8}
y\neq \frac{8}{5}
Solve for y
y=\frac{8}{5}-\frac{4}{5x}
x\neq 0
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4+5yx=8x
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.
4+5yx-8x=0
Subtract 8x from both sides.
5yx-8x=-4
Subtract 4 from both sides. Anything subtracted from zero gives its negation.
\left(5y-8\right)x=-4
Combine all terms containing x.
\frac{\left(5y-8\right)x}{5y-8}=-\frac{4}{5y-8}
Divide both sides by 5y-8.
x=-\frac{4}{5y-8}
Dividing by 5y-8 undoes the multiplication by 5y-8.
x=-\frac{4}{5y-8}\text{, }x\neq 0
Variable x cannot be equal to 0.
4+5yx=8x
Multiply both sides of the equation by x.
5yx=8x-4
Subtract 4 from both sides.
5xy=8x-4
The equation is in standard form.
\frac{5xy}{5x}=\frac{8x-4}{5x}
Divide both sides by 5x.
y=\frac{8x-4}{5x}
Dividing by 5x undoes the multiplication by 5x.
y=\frac{8}{5}-\frac{4}{5x}
Divide 8x-4 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
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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}