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