Let the two integers be [tex] x [/tex] and [tex] y [/tex]
We know that [tex] x [/tex] is 19 more than [tex] 2y [/tex], which means
[tex] x = 2y+19 [/tex]
Also, their product is -44, which means
[tex] xy = -44 [/tex]
We can substitute the expression for [tex] x [/tex] given by the first equation into the second:
[tex] xy = -44 \iff (2y+19)y = -44 \iff 2y^2+19y+44=0 [/tex]
This equation has solutions
[tex] y_1 = -\dfrac{11}{2},\ y_2 = -4 [/tex]
So, if we're looking for an integer solution, we can only choose [tex] y = -4 [/tex]
Which implies
[tex] x = 2(-4)+19 = -8+19 = 11 [/tex]
