An integer is 15 more than 2 tomes another. If the product of two integers is - 27 then find the integers

x = 9 and y = - 3

Step-by-step explanation:

Let's say the first integer is x and the second one is y. Then, if we put the words into mathematical expressions, we get:

x = 15 + 2y

xy = - 27

We can use substitution to solve this system of equations. We put 15 + 2y in for x in xy = - 27:

(15 + 2y) * y = - 27 ⇒ 2y² + 15y = - 27 ⇒ 2y² + 15y + 27 = 0

Now, we have a quadratic to solve, so after some trial and error, we get:

(2y + 9) * (y + 3) = 0

Setting each of these to 0, we get two possible answers for y:

y = - 9/2 or y = - 3.

However, it says that y is an integer, so it can't be - 9/2 and must be - 3. We use this to find x:

x = 15 + 2 * (-3) = 15 - 6 = 9

So, the two numbers are x = 9 and y = - 3.