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