Solve r=-2y{S}_{4}=5

$$r = -2y { S }_{ 4 } = 5$$

Solve for S (complex solution)

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

Steps for Solving Linear Equation

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

$$-2yS=r$$

The equation is in standard form.

$$\left(-2y\right)S=r$$

Divide both sides by -2y.

$$\frac{\left(-2y\right)S}{-2y}=\frac{r}{-2y}$$

Dividing by -2y undoes the multiplication by -2y.

$$S=\frac{r}{-2y}$$

Divide r by -2y.

$$S=-\frac{r}{2y}$$

Solve for S

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

Steps for Solving Linear Equation

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

$$-2yS=r$$

The equation is in standard form.

$$\left(-2y\right)S=r$$

Divide both sides by -2y.

$$\frac{\left(-2y\right)S}{-2y}=\frac{r}{-2y}$$

Dividing by -2y undoes the multiplication by -2y.

$$S=\frac{r}{-2y}$$

Divide r by -2y.

$$S=-\frac{r}{2y}$$

Solve for r

$$r=-2Sy$$