SOLUTION: The question I was given is "The sum of the squares of two numbers is 61 and the sum of those two numbers is 11. Calculate all the possible combinations of two numbers that satisfy

Question 683710: The question I was given is "The sum of the squares of two numbers is 61 and the sum of those two numbers is 11. Calculate all the possible combinations of two numbers that satisfy these statements."
I attempted the question by first writing x+y=11 and x^2 +y^2=61. Therefore y=11-x. Unfortunately I can't understand any of the notes I made in class after that and would really appreciate any advice. Step by step solutions would be amazing as well, thank you.
Found 3 solutions by nerdybill, Alan3354, ReadingBoosters:
Answer by nerdybill(7384)   (Show Source): You can put this solution on YOUR website!
You derived two equations from the problem:
x+y=11 (equation 1)
x^2 +y^2=61 (equation 2)
.
Then, you solved equation 1 for y:
y=11-x
.
NOW, you substitute the above into equation 2 and solve for x:
x^2 +y^2=61
x^2 +(11-x)^2=61
x^2 +(11-x)(11-x)=61
x^2 + 121 - 22x + x^2=61
2x^2 + 121 - 22x = 61
2x^2 - 22x + 121 = 61
2x^2 - 22x + 60 = 0
x^2 - 11x + 30 = 0
(x-5)(x-6) = 0
x = {5, 6}
.
to find y, substitute above back into:
y=11-x
y = {6, 5}
.
answers:
x=5 and y=6
OR
x=6 and y=5

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
x+y=11 and x^2 +y^2=61
-----------
y = 11-x
Sub for y in the 2nd eqn

(x-5)*(x-6) = 0
--> 5 & 6

Answer by ReadingBoosters(3246)   (Show Source): You can put this solution on YOUR website!
From where you left off, substitute...

==> divide the entire equation by 2

(x-6)(x-5)=0
x-6=0, so x=6
AND
x-5=0, so x=5
...
The numbers are 5 and 6.
...
check
25+36=61 and 5+6=11
...
-Reading Boosters
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