Solve for x
x=\frac{8}{3}+\frac{5}{3y}
y\neq 0
Solve for y
y=-\frac{5}{8-3x}
x\neq \frac{8}{3}
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3xy-5=8y
Multiply both sides of the equation by y.
3xy=8y+5
Add 5 to both sides.
3yx=8y+5
The equation is in standard form.
\frac{3yx}{3y}=\frac{8y+5}{3y}
Divide both sides by 3y.
x=\frac{8y+5}{3y}
Dividing by 3y undoes the multiplication by 3y.
x=\frac{8}{3}+\frac{5}{3y}
Divide 8y+5 by 3y.
3xy-5=8y
Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by y.
3xy-5-8y=0
Subtract 8y from both sides.
3xy-8y=5
Add 5 to both sides. Anything plus zero gives itself.
\left(3x-8\right)y=5
Combine all terms containing y.
\frac{\left(3x-8\right)y}{3x-8}=\frac{5}{3x-8}
Divide both sides by 3x-8.
y=\frac{5}{3x-8}
Dividing by 3x-8 undoes the multiplication by 3x-8.
y=\frac{5}{3x-8}\text{, }y\neq 0
Variable y cannot be equal to 0.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
Arithmetic
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Matrix
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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}