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

$y_1 = -\dfrac{11}{2},\ y_2 = -4$

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

Which implies

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