Given that x+2y5𝑥+2𝑦5 = x - 2y, find x : y

Sure, let's solve the given equation step by step.

Given: $x + 2y5 = x - 2y$

First, let's simplify the equation. Notice that the term $2y5$ seems to be a typographical error. It should likely be $2y \cdot 5$ or $10y$. Let's assume it is $10y$:

$x + 10y = x - 2y$

Next, subtract $x$ from both sides of the equation:

$10y = -2y$

Now, add $2y$ to both sides:

$10y + 2y = 0$

Combine like terms:

$12y = 0$

Divide both sides by 12:

$y = 0$

Since $y = 0$, we can substitute $y$ back into the original equation to find $x$:

$x + 10(0) = x - 2(0)$

This simplifies to:

$x = x$

This is always true, which means $x$ can be any value. Therefore, the ratio $x : y$ is undefined because $y = 0$.

So, the solution is: $x : y \text{ is undefined}$