Two integers with a product of 16 and a sum of 10

Answer 1

Suppose the two integers are x and y.

Then the product would be x * y = 16 and the sum would be x + y = 10.

We can then use substitution or elimination methods to solve the system of two equations.

If doing substitution:

x + y = 10 implies that x = 10 - y

Now x * y = 16 turns into (10 - y) * y = 16, meaning 10y - y² = 16.

We can rewrite this to be y² - 10y + 16 = 0.

Factoring we get (y - 2)(y - 8) = 0. Thus, y = 2 or y = 8.

Now since x = 10 - y, x = 10 - 2 = 8 or x = 10 - 8 = 2.

From this, we see that the two integers are 2 and 8.