Solve for x
x=3y-\frac{1}{2}
Solve for y
y=\frac{x}{3}+\frac{1}{6}
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2x-6y+1=0
Use the distributive property to multiply 2 by x-3y.
2x+1=6y
Add 6y to both sides. Anything plus zero gives itself.
2x=6y-1
Subtract 1 from both sides.
\frac{2x}{2}=\frac{6y-1}{2}
Divide both sides by 2.
x=\frac{6y-1}{2}
Dividing by 2 undoes the multiplication by 2.
x=3y-\frac{1}{2}
Divide 6y-1 by 2.
2x-6y+1=0
Use the distributive property to multiply 2 by x-3y.
-6y+1=-2x
Subtract 2x from both sides. Anything subtracted from zero gives its negation.
-6y=-2x-1
Subtract 1 from both sides.
\frac{-6y}{-6}=\frac{-2x-1}{-6}
Divide both sides by -6.
y=\frac{-2x-1}{-6}
Dividing by -6 undoes the multiplication by -6.
y=\frac{x}{3}+\frac{1}{6}
Divide -2x-1 by -6.
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}