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Let integers be x and y

x  + y   = 5

x y   = - 66

x ( 5  - x )  = - 66

5x  - x²   = - 66

x²  - 5 x  + 66   = 0

( x  - 11 ) ( x  + 6 )   = 0

x   = 11 , x   = - 6

Integers are 6 , - 11

11 & -6................

11 and -6 are the two integers whose sum is 5 and product is -66.

Two integers whose sum is 5 and product is -66: 11 and -6

if the sum of the two integers, a and b, is 5:

a + b = 5

and if the product of the two integers is -66:

a * b = -66

we can find a in terms of b and plug it back into another equation:

a + b = 5

a = 5 - b

If a = b - 5 in this equation, we have to assume it is true in the other one to find the values that satisfy the system, therefore:

a * b = -66

(5 - b) * b = -66

-b^2 + 5b + 66 = 0

b^2 - 5b - 66 = 0

(b - 11) (b + 6) = 0

your two numbers will be -6 and 11

x + y = 5

xy = -66

Solve the system of equations.

x = -11, y = 6

A+B=5  >>> B=5-A  

AB= -66

A(5-A)=-66

5A - A² = -66

0 = A² - 5A -66

0 = (A+6)(A-11)

A= -6, 11 and B= 11, -6  by the pairing

Product is -66 and sum is +5 so -6 and +11 are the two numbers

x+y=5

xy=-66

So

x=5-y  and y=(-66/x)

x=(5x+66)/x

x²=5x+66

x²-5x-66=0

x=-6 so y=11

x=11 so y=-6

x+y = 5

xy = –66

y = 5 – x

x(5–x) = –66

5x – x² = –66

x² – 5x – 66 = 0

(x + 6)(x – 11) = 0

x = 11, –6

y = –6, 11

-6 and 11