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

Mathematics

1 answer:

andre [41]3 years ago

7 0

Answer:

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.

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