Solve for x
x=-\frac{3\left(y-3\right)}{2\left(y+2\right)}
y\neq -2
Solve for y
y=-\frac{4x-9}{2x+3}
x\neq -\frac{3}{2}
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2xy+4x+3y+6=15
Use the distributive property to multiply 2x+3 by y+2.
2xy+4x+6=15-3y
Subtract 3y from both sides.
2xy+4x=15-3y-6
Subtract 6 from both sides.
2xy+4x=9-3y
Subtract 6 from 15 to get 9.
\left(2y+4\right)x=9-3y
Combine all terms containing x.
\frac{\left(2y+4\right)x}{2y+4}=\frac{9-3y}{2y+4}
Divide both sides by 2y+4.
x=\frac{9-3y}{2y+4}
Dividing by 2y+4 undoes the multiplication by 2y+4.
x=\frac{3\left(3-y\right)}{2\left(y+2\right)}
Divide 9-3y by 2y+4.
2xy+4x+3y+6=15
Use the distributive property to multiply 2x+3 by y+2.
2xy+3y+6=15-4x
Subtract 4x from both sides.
2xy+3y=15-4x-6
Subtract 6 from both sides.
2xy+3y=9-4x
Subtract 6 from 15 to get 9.
\left(2x+3\right)y=9-4x
Combine all terms containing y.
\frac{\left(2x+3\right)y}{2x+3}=\frac{9-4x}{2x+3}
Divide both sides by 2x+3.
y=\frac{9-4x}{2x+3}
Dividing by 2x+3 undoes the multiplication by 2x+3.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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}