Solve r^2x=y-2

$$r ^ { 2 } x = y - 2$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{y-2}{r^{2}}\text{, }&r\neq 0\\x\in \mathrm{C}\text{, }&y=2\text{ and }r=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$r^{2}x=y-2$$

Divide both sides by r^{2}.

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

Dividing by r^{2} undoes the multiplication by r^{2}.

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

Solve for x

$$\left\{\begin{matrix}x=\frac{y-2}{r^{2}}\text{, }&r\neq 0\\x\in \mathrm{R}\text{, }&y=2\text{ and }r=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$r^{2}x=y-2$$

Divide both sides by r^{2}.

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

Dividing by r^{2} undoes the multiplication by r^{2}.

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

Solve for r (complex solution)

$$\left\{\begin{matrix}r=-x^{-\frac{1}{2}}\sqrt{y-2}\text{; }r=x^{-\frac{1}{2}}\sqrt{y-2}\text{, }&x\neq 0\\r\in \mathrm{C}\text{, }&y=2\text{ and }x=0\end{matrix}\right.$$

Solve for r

$$\left\{\begin{matrix}r=\sqrt{\frac{y-2}{x}}\text{; }r=-\sqrt{\frac{y-2}{x}}\text{, }&\left(y\geq 2\text{ and }x>0\right)\text{ or }\left(y\leq 2\text{ and }x<0\right)\\r\in \mathrm{R}\text{, }&y=2\text{ and }x=0\end{matrix}\right.$$