Solve for f
\left\{\begin{matrix}f=-\frac{5-y}{2\left(x-3\right)}\text{, }&x\neq 3\\f\in \mathrm{R}\text{, }&y=5\text{ and }x=3\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=-\frac{5-6f-y}{2f}\text{, }&f\neq 0\\x\in \mathrm{R}\text{, }&y=5\text{ and }f=0\end{matrix}\right.
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y=2fx-6f+5
Use the distributive property to multiply 2f by x-3.
2fx-6f+5=y
Swap sides so that all variable terms are on the left hand side.
2fx-6f=y-5
Subtract 5 from both sides.
\left(2x-6\right)f=y-5
Combine all terms containing f.
\frac{\left(2x-6\right)f}{2x-6}=\frac{y-5}{2x-6}
Divide both sides by 2x-6.
f=\frac{y-5}{2x-6}
Dividing by 2x-6 undoes the multiplication by 2x-6.
f=\frac{y-5}{2\left(x-3\right)}
Divide y-5 by 2x-6.
y=2fx-6f+5
Use the distributive property to multiply 2f by x-3.
2fx-6f+5=y
Swap sides so that all variable terms are on the left hand side.
2fx+5=y+6f
Add 6f to both sides.
2fx=y+6f-5
Subtract 5 from both sides.
\frac{2fx}{2f}=\frac{y+6f-5}{2f}
Divide both sides by 2f.
x=\frac{y+6f-5}{2f}
Dividing by 2f undoes the multiplication by 2f.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
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Matrix
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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}