Solve for k (complex solution)
\left\{\begin{matrix}k=\frac{y+3}{x+1}\text{, }&x\neq -1\\k\in \mathrm{C}\text{, }&y=-3\text{ and }x=-1\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}x=-\frac{-y+k-3}{k}\text{, }&k\neq 0\\x\in \mathrm{C}\text{, }&y=-3\text{ and }k=0\end{matrix}\right.
Solve for k
\left\{\begin{matrix}k=\frac{y+3}{x+1}\text{, }&x\neq -1\\k\in \mathrm{R}\text{, }&y=-3\text{ and }x=-1\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=-\frac{-y+k-3}{k}\text{, }&k\neq 0\\x\in \mathrm{R}\text{, }&y=-3\text{ and }k=0\end{matrix}\right.
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kx-3+k=y
Swap sides so that all variable terms are on the left hand side.
kx+k=y+3
Add 3 to both sides.
\left(x+1\right)k=y+3
Combine all terms containing k.
\frac{\left(x+1\right)k}{x+1}=\frac{y+3}{x+1}
Divide both sides by x+1.
k=\frac{y+3}{x+1}
Dividing by x+1 undoes the multiplication by x+1.
kx-3+k=y
Swap sides so that all variable terms are on the left hand side.
kx+k=y+3
Add 3 to both sides.
kx=y+3-k
Subtract k from both sides.
kx=y-k+3
The equation is in standard form.
\frac{kx}{k}=\frac{y-k+3}{k}
Divide both sides by k.
x=\frac{y-k+3}{k}
Dividing by k undoes the multiplication by k.
kx-3+k=y
Swap sides so that all variable terms are on the left hand side.
kx+k=y+3
Add 3 to both sides.
\left(x+1\right)k=y+3
Combine all terms containing k.
\frac{\left(x+1\right)k}{x+1}=\frac{y+3}{x+1}
Divide both sides by x+1.
k=\frac{y+3}{x+1}
Dividing by x+1 undoes the multiplication by x+1.
kx-3+k=y
Swap sides so that all variable terms are on the left hand side.
kx+k=y+3
Add 3 to both sides.
kx=y+3-k
Subtract k from both sides.
kx=y-k+3
The equation is in standard form.
\frac{kx}{k}=\frac{y-k+3}{k}
Divide both sides by k.
x=\frac{y-k+3}{k}
Dividing by k undoes the multiplication by k.
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Simultaneous equation
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Integration
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Limits
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