Solve -yx^2/θz=1

$$\frac{ -y { x }^{ 2 } }{ \theta z } = 1$$

Solve for y

$$y=-\frac{z\theta }{x^{2}}$$

$$x\neq 0\text{ and }\theta \neq 0\text{ and }z\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by z\theta .

$$\left(-y\right)x^{2}=z\theta$$

Reorder the terms.

$$-yx^{2}=z\theta$$

The equation is in standard form.

$$\left(-x^{2}\right)y=z\theta$$

Divide both sides by -x^{2}.

$$\frac{\left(-x^{2}\right)y}{-x^{2}}=\frac{z\theta }{-x^{2}}$$

Dividing by -x^{2} undoes the multiplication by -x^{2}.

$$y=\frac{z\theta }{-x^{2}}$$

Divide z\theta by -x^{2}.

$$y=-\frac{z\theta }{x^{2}}$$

Solve for x (complex solution)

$$x=-iy^{-\frac{1}{2}}\sqrt{z}\sqrt{\theta }$$

$$x=iy^{-\frac{1}{2}}\sqrt{z}\sqrt{\theta }\text{, }y\neq 0\text{ and }\theta \neq 0\text{ and }z\neq 0$$

Solve for x

$$x=\sqrt{-\frac{z\theta }{y}}$$

$$x=-\sqrt{-\frac{z\theta }{y}}\text{, }\left(y<0\text{ and }\theta <0\text{ and }z<0\right)\text{ or }\left(y>0\text{ and }z<0\text{ and }\theta >0\right)\text{ or }\left(y>0\text{ and }\theta <0\text{ and }z>0\right)\text{ or }\left(y<0\text{ and }z>0\text{ and }\theta >0\right)$$