Solve y^1-10xy^2=0

$$y ^ { 1 } - 10 x y ^ { 2 } = 0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{1}{10y}\text{, }&y\neq 0\\x\in \mathrm{C}\text{, }&y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Calculate y to the power of 1 and get y.

$$y-10xy^{2}=0$$

Subtract y from both sides. Anything subtracted from zero gives its negation.

$$-10xy^{2}=-y$$

The equation is in standard form.

$$\left(-10y^{2}\right)x=-y$$

Divide both sides by -10y^{2}.

$$\frac{\left(-10y^{2}\right)x}{-10y^{2}}=-\frac{y}{-10y^{2}}$$

Dividing by -10y^{2} undoes the multiplication by -10y^{2}.

$$x=-\frac{y}{-10y^{2}}$$

Divide -y by -10y^{2}.

$$x=\frac{1}{10y}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{1}{10y}\text{, }&y\neq 0\\x\in \mathrm{R}\text{, }&y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Calculate y to the power of 1 and get y.

$$y-10xy^{2}=0$$

Subtract y from both sides. Anything subtracted from zero gives its negation.

$$-10xy^{2}=-y$$

The equation is in standard form.

$$\left(-10y^{2}\right)x=-y$$

Divide both sides by -10y^{2}.

$$\frac{\left(-10y^{2}\right)x}{-10y^{2}}=-\frac{y}{-10y^{2}}$$

Dividing by -10y^{2} undoes the multiplication by -10y^{2}.

$$x=-\frac{y}{-10y^{2}}$$

Divide -y by -10y^{2}.

$$x=\frac{1}{10y}$$

Solve for y

$$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y=\frac{1}{10x}\text{, }&x\neq 0\end{matrix}\right.$$