SOLUTION: The sum of two numbers is 7. If three times the square of the first number is added to twice the square of the second number, the sum is 59. Find the numbers.

Question 662660: The sum of two numbers is 7. If three times the square of the first number is added to twice the square of the second number, the sum is 59. Find the numbers.
Answer by ReadingBoosters(3246) (Show Source): You can put this solution on YOUR website!
x+y=7
3x^2 + 2y^2 = 59
3(-y+7)(-y+7) + 2y^2 = 59
3(y^2-7y-7y+49) + 2y^2 = 59
3y^2 - 42y + 147 + 2y^2 = 59
5y^2 - 42y + 88 = 0
(5y-22)(y-4) = 0
5y-22=0 so y = 22/5
y-4=0 so y = 4
Two possibilities
if y = 4, x = 7-4=3
if y = 22/5, x = 7 - 22/5 = 13/5
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