Solve for c (complex solution)
\left\{\begin{matrix}c=-\frac{Σ\left(mx-y\right)}{n}\text{, }&n\neq 0\\c\in \mathrm{C}\text{, }&\left(m=\frac{y}{x}\text{ and }x\neq 0\text{ and }n=0\right)\text{ or }\left(y=0\text{ and }x=0\text{ and }n=0\right)\text{ or }\left(Σ=0\text{ and }n=0\right)\end{matrix}\right.
Solve for m (complex solution)
\left\{\begin{matrix}m=-\frac{cn-yΣ}{xΣ}\text{, }&x\neq 0\text{ and }Σ\neq 0\\m\in \mathrm{C}\text{, }&\left(c=\frac{yΣ}{n}\text{ and }n\neq 0\text{ and }x=0\right)\text{ or }\left(y=0\text{ and }n=0\text{ and }x=0\right)\text{ or }\left(c=0\text{ and }n\neq 0\text{ and }Σ=0\text{ and }x\neq 0\right)\text{ or }\left(Σ=0\text{ and }n=0\right)\end{matrix}\right.
Solve for c
\left\{\begin{matrix}c=-\frac{Σ\left(mx-y\right)}{n}\text{, }&n\neq 0\\c\in \mathrm{R}\text{, }&\left(m=\frac{y}{x}\text{ and }x\neq 0\text{ and }n=0\right)\text{ or }\left(y=0\text{ and }x=0\text{ and }n=0\right)\text{ or }\left(Σ=0\text{ and }n=0\right)\end{matrix}\right.
Solve for m
\left\{\begin{matrix}m=-\frac{cn-yΣ}{xΣ}\text{, }&x\neq 0\text{ and }Σ\neq 0\\m\in \mathrm{R}\text{, }&\left(c=\frac{yΣ}{n}\text{ and }n\neq 0\text{ and }x=0\right)\text{ or }\left(y=0\text{ and }n=0\text{ and }x=0\right)\text{ or }\left(c=0\text{ and }n\neq 0\text{ and }Σ=0\text{ and }x\neq 0\right)\text{ or }\left(Σ=0\text{ and }n=0\right)\end{matrix}\right.
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cn=Σy-mΣx
Subtract mΣx from both sides.
cn=-mxΣ+yΣ
Reorder the terms.
nc=yΣ-mxΣ
The equation is in standard form.
\frac{nc}{n}=\frac{Σ\left(y-mx\right)}{n}
Divide both sides by n.
c=\frac{Σ\left(y-mx\right)}{n}
Dividing by n undoes the multiplication by n.
mΣx=Σy-cn
Subtract cn from both sides.
xΣm=yΣ-cn
The equation is in standard form.
\frac{xΣm}{xΣ}=\frac{yΣ-cn}{xΣ}
Divide both sides by Σx.
m=\frac{yΣ-cn}{xΣ}
Dividing by Σx undoes the multiplication by Σx.
cn=Σy-mΣx
Subtract mΣx from both sides.
cn=-mxΣ+yΣ
Reorder the terms.
nc=yΣ-mxΣ
The equation is in standard form.
\frac{nc}{n}=\frac{Σ\left(y-mx\right)}{n}
Divide both sides by n.
c=\frac{Σ\left(y-mx\right)}{n}
Dividing by n undoes the multiplication by n.
mΣx=Σy-cn
Subtract cn from both sides.
xΣm=yΣ-cn
The equation is in standard form.
\frac{xΣm}{xΣ}=\frac{yΣ-cn}{xΣ}
Divide both sides by Σx.
m=\frac{yΣ-cn}{xΣ}
Dividing by Σx undoes the multiplication by Σx.
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
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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}