Solve for x
x=\frac{2y}{3}+\frac{3}{2}
Solve for y
y=\frac{3x}{2}-\frac{9}{4}
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6x-9=4y
Add 4y to both sides. Anything plus zero gives itself.
6x=4y+9
Add 9 to both sides.
\frac{6x}{6}=\frac{4y+9}{6}
Divide both sides by 6.
x=\frac{4y+9}{6}
Dividing by 6 undoes the multiplication by 6.
x=\frac{2y}{3}+\frac{3}{2}
Divide 4y+9 by 6.
-4y-9=-6x
Subtract 6x from both sides. Anything subtracted from zero gives its negation.
-4y=-6x+9
Add 9 to both sides.
-4y=9-6x
The equation is in standard form.
\frac{-4y}{-4}=\frac{9-6x}{-4}
Divide both sides by -4.
y=\frac{9-6x}{-4}
Dividing by -4 undoes the multiplication by -4.
y=\frac{3x}{2}-\frac{9}{4}
Divide -6x+9 by -4.
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}