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

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.