Question

(2x-3y)(x+5y)=0 where x>0 and y>0

Find the ratio x:y
Give your answer in its simplest form.

Answer 1

Answer: We can use the distributive property to expand the left side of the equation:

2xx + 2x5y - 3yx - 3y5y = 0

Then, combine like terms:

2x^2 + 10xy - 3xy - 15y^2 = 0

Now we can add 3xy + 15y^2 on both sides of the equation to get:

2x^2 + 10xy = 0

We know that x and y are positive, so we can divide both sides by 2:

x^2 + 5xy = 0

and since x>0, we can divide both sides by x:

x + 5y = 0

So the ratio x:y = x/(-5y) = -x/5y.

To simplify we can divide x by -x and 5y by 5y and get the final answer as

x:y = -1:

Explanation:

Answer 2

Answer:
`3:2`

Explanation:

Using the zero-product property, we know that
`2x-3y=0` or
`x+5y=0`. We can rearrange these cases to yield
`x=(3)/(2)y` and
`x=-5y`.

However, since
`x` and
`y` have the same sign, we neglect the case
`x=-5y`. This means
`x=(3)/(2)y`.

`x=(3)/(2)y \implies (x)/(y)=(3)/(2) \implies x:y=3:2`