Problem:
The sum of two integers is -11 and their product is -80. Find the two integers.

Solution:
To solve this problem, we can use the following steps:

Step 1: Set up the equations using the given information
Let x and y be the two integers. We know that:

x + y = -11 (sum of the two integers is -11)

xy = -80 (product of the two integers is -80)

Step 2: Solve for one variable in terms of the other
We can use the first equation to solve for one variable in terms of the other. Let's solve for x:

x + y = -11

x = -y - 11

Step 3: Substitute the expression from Step 2 into the second equation
Now we can substitute the expression we found for x into the second equation:

xy = -80

(-y - 11)y = -80

Simplifying this equation, we get:

-y^2 - 11y = -80

y^2 + 11y - 80 = 0

Step 4: Solve the quadratic equation
We now have a quadratic equation in y. We can solve this equation using factoring or the quadratic formula. Factoring gives us:

(y + 16)(y - 5) = 0

So y = -16 or y = 5.

Step 5: Find the corresponding value of x
Finally, we can use the expression we found for x in Step 2 to find the corresponding value of x for each value of y:

If y = -16, then x = -y - 11 = 5
If y = 5, then x = -y - 11 = -16

Answer:
The two integers are 5 and -16.

Sol:-
i) 5×16=80
=16×(-5)=-80

ii) 16-5=11
= 5+(-16)= -11