SOLUTION: The sum of squares of two natural number is 13. The sum of 2 times of the smaller and 5 times of the larger is 19. Find the numbers. Please help

Question 1024060: The sum of squares of two natural number is 13.
The sum of 2 times of the smaller and 5 times of the larger is 19.
Find the numbers. Please help
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
x^2 + y^2 = 13
2x + 5y = 19
:
solve second equation for x
:
x = (19-5y) / 2
:
substitute for x in first equation
:
( (19-5y)^2 / 4 ) + y^2 = 13
:
( (361 - 190y + 25y^2) / 4 ) + y^2 = 13
:
361 -190y +25y^2 + 4y^2 = 52
:
29y^2 -190y +309 = 0
:
use quadratic equation
:
y = ( 190 + sqrt(190^2 -4*29*309) ) / (2*29) = 3.551724138
:
y = ( 190 - sqrt(190^2 -4*29*309) ) / (2*29) = 3
:
2x + (5*3) = 19
x = 2
:
*******************************
The two numbers are 2 and 3
*******************************
we check the answer by substituting in the first equation
2^2 + 3^2 = 13
4 + 9 = 13
13 = 13
our answer checks

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