Solve y=-operatorname{coten}(θ)x

$$y = - \operatorname { coten } ( \theta ) x$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{y\tan(en)}{\theta }\text{, }&\nexists n_{3}\in \mathrm{Z}\text{ : }n=\frac{\pi n_{3}}{2e}\text{ and }\theta \neq 0\\x\in \mathrm{R}\text{, }&\left(y=0\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }n=\frac{\pi n_{1}}{e}\text{ and }\theta =0\right)\text{ or }\left(y=0\text{ and }\exists n_{2}\in \mathrm{Z}\text{ : }n=\frac{\pi n_{2}}{e}+\frac{\pi }{2e}\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$\left(-\cot(en)\right)\theta x=y$$

The equation is in standard form.

$$\left(-\theta \cot(en)\right)x=y$$

Divide both sides by -\cot(en)\theta .

$$\frac{\left(-\theta \cot(en)\right)x}{-\theta \cot(en)}=\frac{y}{-\theta \cot(en)}$$

Dividing by -\cot(en)\theta undoes the multiplication by -\cot(en)\theta .

$$x=\frac{y}{-\theta \cot(en)}$$

Divide y by -\cot(en)\theta .

$$x=-\frac{y\tan(en)}{\theta }$$

Solve for n

$$n\neq \frac{\pi n_{1}}{e}$$

$$\forall n_{1}\in \mathrm{Z}$$

$$\left(\theta =0\text{ or }x=0\right)\text{ and }y=0$$