SOLUTION: The sum of two numbers is 15.The sum of their squares is 9 more than 13 times the larger number.Find the numbers.

Question 1092272: The sum of two numbers is 15.The sum of their squares is 9 more than 13 times the larger number.Find the numbers.
Found 2 solutions by richwmiller, greenestamps:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
x+y=15
x^2+y^2=13*x+9
Answer by greenestamps(13206) (Show Source): You can put this solution on YOUR website!

I nearly always find it easier to solve problems like this using a single variable instead of two. Given that the sum of the two numbers is 15, I would do

let x = large number
then (15-x) = smaller number

The sum of the squares of the two numbers is 9 more than 13 times the larger number:

This gives us two potential solutions:

(1) x = 8; 15-x = 7 OR
(2) x = 27/2; 15-x = 3/2

Since our solution method involved squaring expressions, we need to check to see which of the solutions actually satisfy the original problem.

For the first...

and

So that solution is valid.

For the second...

This solution is also valid.

So there are two solutions to the problem: 8 and 7; or 27/2 and 3/2.
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