Solve rx+ry=0

$$r x + r y = 0$$

Solve for r

$$\left\{\begin{matrix}\\r=0\text{, }&\text{unconditionally}\\r\in \mathrm{R}\text{, }&x=-y\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine all terms containing r.

$$\left(x+y\right)r=0$$

Divide 0 by x+y.

$$r=0$$

Solve for x

$$\left\{\begin{matrix}\\x=-y\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&r=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$rx=-ry$$

Divide both sides by r.

$$\frac{rx}{r}=-\frac{ry}{r}$$

Dividing by r undoes the multiplication by r.

$$x=-\frac{ry}{r}$$

Divide -ry by r.

$$x=-y$$