Solve for x
x=\frac{3y}{2}
Solve for y
y=\frac{2x}{3}
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4x+7y-4y-6x=0
Multiply both sides of the equation by 2.
4x+3y-6x=0
Combine 7y and -4y to get 3y.
-2x+3y=0
Combine 4x and -6x to get -2x.
-2x=-3y
Subtract 3y from both sides. Anything subtracted from zero gives its negation.
\frac{-2x}{-2}=-\frac{3y}{-2}
Divide both sides by -2.
x=-\frac{3y}{-2}
Dividing by -2 undoes the multiplication by -2.
x=\frac{3y}{2}
Divide -3y by -2.
4x+7y-4y-6x=0
Multiply both sides of the equation by 2.
4x+3y-6x=0
Combine 7y and -4y to get 3y.
-2x+3y=0
Combine 4x and -6x to get -2x.
3y=2x
Add 2x to both sides. Anything plus zero gives itself.
\frac{3y}{3}=\frac{2x}{3}
Divide both sides by 3.
y=\frac{2x}{3}
Dividing by 3 undoes the multiplication by 3.
Examples
Quadratic equation
{ 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}