Question

An integer is 19 more than 2 times another if the product of the two integers is -44

Answer 1

Let the two integers be
`x` and
`y`

We know that
`x` is 19 more than
`2y`, which means

`x = 2y+19`

Also, their product is -44, which means

`xy = -44`

We can substitute the expression for
`x` given by the first equation into the second:

`xy = -44 \iff (2y+19)y = -44 \iff 2y^2+19y+44=0`

This equation has solutions

`y_1 = -(11)/(2),\ y_2 = -4`

So, if we're looking for an integer solution, we can only choose
`y = -4`

Which implies

`x = 2(-4)+19 = -8+19 = 11`