SOLUTION: I have a word problem that I would like help simplifying. The sum of 2 numbers is 20,and the sum of their squares is 218.Find the numbers. I have created equations of x+y=20

Algebra ->  Human-and-algebraic-language -> SOLUTION: I have a word problem that I would like help simplifying. The sum of 2 numbers is 20,and the sum of their squares is 218.Find the numbers. I have created equations of x+y=20      Log On


   

Question 331683: I have a word problem that I would like help simplifying.
The sum of 2 numbers is 20,and the sum of their squares is 218.Find the numbers.
I have created equations of x+y=20 and x*x+y*y= 218. but I am assuming I need to break down the second equation to substitute the value of 20 for the term x+y.
Any help would be great
Thanks
Steve
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
x + y = 20 ___ y = 20 - x

substituting ___ x^2 + (20 - x)^2 = 218 ___ x^2 + 400 - 40x + x^2 = 218

x^2 - 20x + 91 = 0 ___ (x - 13)(x - 7) = 0

x = 13 (or 7) and y equals the other one