# The sum of 2 numbers is 22 and their product is 117. Find the numbers.

Let us say the two numbers are P and Q.

Then;

`P+Q = 22` -----(1)

` PQ = 117` -----(2)

From (1) `P = 22-Q`

`PQ = 117`

`(22-Q)Q = 117`

`22Q-Q^2-117 = 0`

`Q^2-22Q+117 = 0`

`Q = ((-22)+-sqrt((-22)^2-4*1*117))/(2*1)`

`Q = 13` and `Q = 9`

*So the two numbers are 13 and 9.*

There are two variables in this. So mostly there will be two equations.

the first one talks about the sum which is addition. we do not know the two numbers but we know the sum of them which is 22. so if the variables were x and y then the first equation would be:

x + y = 22

the second equation has to do with multiplication and we do not know the numbers but we do know the product so the second equation is:

x * y = 117

now you can either use the sustitution or the elimination method.

The answers are 13 and 9.

I will not give the steps so that u can learn without just copying it but i gave you the answers so that you can see if your answer is correct.

If you are not sure about an answer about something just plug in the variables

9 and 13

2 Equations:

x+y=22

xy=117

From first equation, x=22-y

Plug it into the second equation:

y(22-y)=117

Simplify, subtract 117 from both sides, multiply -1 to both sides.

y^2-22y+117=0

Factor.

(y-9)(y-13)=0

Therefore, y: {9, 13}