SOLUTION: One number is 9 more than 2 times another. Their product is 5 more than 3 times their sum. Find the numbers. Answer in the form of paired points with the lowest of the two inte

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: One number is 9 more than 2 times another. Their product is 5 more than 3 times their sum. Find the numbers. Answer in the form of paired points with the lowest of the two inte      Log On


   

Question 959492: One number is 9 more than 2 times another. Their product is 5 more than 3 times their sum. Find the numbers. Answer in the form of paired points with the lowest of the two integers first
Answer by CubeyThePenguin(3113) About Me  (Show Source):
You can put this solution on YOUR website!
x = larger number
y = smaller number

x = 2y + 9
xy = 3(x + y) + 5

Substitute x into the second equation.

(2y + 9)(y) = 3(2y + 9 + y) + 5
2y^2 + 9y = 3(3y + 9) + 5
2y^2 + 9y = 9y + 32
2y^2 = 32
y^2 = 16
y = 4 or -4

The integers are (x, y) = (17, 4) or (1, -4)