Solve for x
x=-\frac{y}{2}-1
Solve for y
y=-2x-2
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y-2=\frac{-2}{-1-\left(-2\right)}\left(x-\left(-2\right)\right)
Subtract 2 from 0 to get -2.
y-2=\frac{-2}{-1+2}\left(x-\left(-2\right)\right)
The opposite of -2 is 2.
y-2=\frac{-2}{1}\left(x-\left(-2\right)\right)
Add -1 and 2 to get 1.
y-2=-2\left(x-\left(-2\right)\right)
Anything divided by one gives itself.
y-2=-2\left(x+2\right)
The opposite of -2 is 2.
y-2=-2x-4
Use the distributive property to multiply -2 by x+2.
-2x-4=y-2
Swap sides so that all variable terms are on the left hand side.
-2x=y-2+4
Add 4 to both sides.
-2x=y+2
Add -2 and 4 to get 2.
\frac{-2x}{-2}=\frac{y+2}{-2}
Divide both sides by -2.
x=\frac{y+2}{-2}
Dividing by -2 undoes the multiplication by -2.
x=-\frac{y}{2}-1
Divide y+2 by -2.
y-2=\frac{-2}{-1-\left(-2\right)}\left(x-\left(-2\right)\right)
Subtract 2 from 0 to get -2.
y-2=\frac{-2}{-1+2}\left(x-\left(-2\right)\right)
The opposite of -2 is 2.
y-2=\frac{-2}{1}\left(x-\left(-2\right)\right)
Add -1 and 2 to get 1.
y-2=-2\left(x-\left(-2\right)\right)
Anything divided by one gives itself.
y-2=-2\left(x+2\right)
The opposite of -2 is 2.
y-2=-2x-4
Use the distributive property to multiply -2 by x+2.
y=-2x-4+2
Add 2 to both sides.
y=-2x-2
Add -4 and 2 to get -2.
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}