Solve for f
\left\{\begin{matrix}f=-\frac{2-y}{2\left(x-2\right)}\text{, }&x\neq 2\\f\in \mathrm{R}\text{, }&y=2\text{ and }x=2\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=\frac{y+4f-2}{2f}\text{, }&f\neq 0\\x\in \mathrm{R}\text{, }&y=2\text{ and }f=0\end{matrix}\right.
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y=2fx-4f+2
Use the distributive property to multiply 2f by x-2.
2fx-4f+2=y
Swap sides so that all variable terms are on the left hand side.
2fx-4f=y-2
Subtract 2 from both sides.
\left(2x-4\right)f=y-2
Combine all terms containing f.
\frac{\left(2x-4\right)f}{2x-4}=\frac{y-2}{2x-4}
Divide both sides by 2x-4.
f=\frac{y-2}{2x-4}
Dividing by 2x-4 undoes the multiplication by 2x-4.
f=\frac{y-2}{2\left(x-2\right)}
Divide y-2 by 2x-4.
y=2fx-4f+2
Use the distributive property to multiply 2f by x-2.
2fx-4f+2=y
Swap sides so that all variable terms are on the left hand side.
2fx+2=y+4f
Add 4f to both sides.
2fx=y+4f-2
Subtract 2 from both sides.
\frac{2fx}{2f}=\frac{y+4f-2}{2f}
Divide both sides by 2f.
x=\frac{y+4f-2}{2f}
Dividing by 2f undoes the multiplication by 2f.
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}