SOLUTION: The sum of two Numbers is 16. The sum of their squares exceeds 13 times the largar number by 4. What are the Numbers ?

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Question 962426: The sum of two Numbers is 16. The sum of their squares exceeds 13 times the largar number by 4. What are the Numbers ?
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
x + y = 16
x^2 + y^2 = 13y +4
note that y is the larger number
solve first equation for x
x = 16 -y
now substitute for x in second equation
(16-y)^2 + y^2 = 13y +4
256 -32y +y^2 +y^2 = 13y + 4
2y^2 -45y +252 = 0
factor equation
(2y-21) * (y-12) = 0
y = 10.5 or 12
we have two solutions
x = 4, y = 12
x = 5.5, y = 10.5