Solve for x
x=-\frac{y}{6}
Solve for y
y=-6x
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\frac{x-0}{\frac{1}{2}}=\frac{y-0}{-3-0}
Subtract 0 from \frac{1}{2} to get \frac{1}{2}.
\frac{x-0}{\frac{1}{2}}=\frac{y-0}{-3}
Subtract 0 from -3 to get -3.
\frac{x}{\frac{1}{2}}-\frac{0}{\frac{1}{2}}=\frac{y-0}{-3}
Divide each term of x-0 by \frac{1}{2} to get \frac{x}{\frac{1}{2}}-\frac{0}{\frac{1}{2}}.
\frac{x}{\frac{1}{2}}+0=\frac{y-0}{-3}
Zero divided by any non-zero number gives zero.
\frac{x}{\frac{1}{2}}=\frac{y-0}{-3}
Anything plus zero gives itself.
\frac{x}{\frac{1}{2}}=-\frac{1}{3}y-0
Divide each term of y-0 by -3 to get -\frac{1}{3}y-0.
\frac{x}{\frac{1}{2}}=-\frac{1}{3}y
Reorder the terms.
2x=-\frac{y}{3}
The equation is in standard form.
\frac{2x}{2}=-\frac{\frac{y}{3}}{2}
Divide both sides by 2.
x=-\frac{\frac{y}{3}}{2}
Dividing by 2 undoes the multiplication by 2.
x=-\frac{y}{6}
Divide -\frac{y}{3} by 2.
\frac{x-0}{\frac{1}{2}}=\frac{y-0}{-3-0}
Subtract 0 from \frac{1}{2} to get \frac{1}{2}.
\frac{x-0}{\frac{1}{2}}=\frac{y-0}{-3}
Subtract 0 from -3 to get -3.
\frac{x}{\frac{1}{2}}-\frac{0}{\frac{1}{2}}=\frac{y-0}{-3}
Divide each term of x-0 by \frac{1}{2} to get \frac{x}{\frac{1}{2}}-\frac{0}{\frac{1}{2}}.
\frac{x}{\frac{1}{2}}+0=\frac{y-0}{-3}
Zero divided by any non-zero number gives zero.
\frac{x}{\frac{1}{2}}=\frac{y-0}{-3}
Anything plus zero gives itself.
\frac{x}{\frac{1}{2}}=-\frac{1}{3}y-0
Divide each term of y-0 by -3 to get -\frac{1}{3}y-0.
-\frac{1}{3}y-0=\frac{x}{\frac{1}{2}}
Swap sides so that all variable terms are on the left hand side.
-\frac{1}{3}y=\frac{x}{\frac{1}{2}}+0
Add 0 to both sides.
-\frac{1}{3}y=\frac{x}{\frac{1}{2}}
Anything plus zero gives itself.
-\frac{1}{3}y=2x
The equation is in standard form.
\frac{-\frac{1}{3}y}{-\frac{1}{3}}=\frac{2x}{-\frac{1}{3}}
Multiply both sides by -3.
y=\frac{2x}{-\frac{1}{3}}
Dividing by -\frac{1}{3} undoes the multiplication by -\frac{1}{3}.
y=-6x
Divide 2x by -\frac{1}{3} by multiplying 2x by the reciprocal of -\frac{1}{3}.
Examples
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{ 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}