Question

Find two integers whose sum is 2 and whose product is -24

Answer 1

The integers would be x and y.
Therefore, we can suggest this system of equations:
x+y=2
xy=-24
We can solve this system of equations by substitution method.
x+y=2;      ⇒y=(2-x)
then:

x(2-x)=-24
2x-x²=-24
x²-2x-24=0

x=[2⁺₋√(4+96)]/2=(2⁺₋10)/2
we would have two possible solutions:
x₁=(2-10)/2=-4    ⇒y₁=(2-x)=2+4=6
x₂=(2+10)/2=6    ⇒y₂=(2-x)=2-6=-4

We can see the numbers would be -4 and 6.

Answer: the numbers would be: -4 and 6.