SOLUTION: Suppose that x and y are positive numbers with xy=1/9, x(y+1)=7/9, y(x+1)=5/18. What is the value of (x+1)(y+1)?

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Question 1071819: Suppose that x and y are positive numbers with xy=1/9, x(y+1)=7/9, y(x+1)=5/18. What is the value of (x+1)(y+1)?
Found 3 solutions by Fombitz, rothauserc, ikleyn:
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website!

So,

Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website!
1) xy = 1/9
2) x(y+1) = 7/9
3) y(x+1) = 5/18
:
using equation 2
:
xy + x = 7/9
:
use equation 1 and substitute for xy in equation 2
:
(1/9) + x = (7/9)
:
x = (7/9) - (1/9) = 6/9 = 2/3
:
use equation 1 and equation 3, subsitute for xy in equation 3
:
yx + y = 5/18
:
(1/9) + y = (5/18) - (1/9) = (3/18) = (1/6)
:
Note that multiplication is communitive, that is, yx = xy
:
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(x+1) * (y+1) = ( (2/3) + 1 ) * ( (1/6) + 1 ) = (5/3) * (7/6) = (35 / 18)
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:

Answer by ikleyn(52794)   (Show Source):
You can put this solution on YOUR website!
.
Suppose that x and y are positive numbers with xy=1/9, x(y+1)=7/9, y(x+1)=5/18. What is the value of (x+1)(y+1)?
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x(y+1)=7/9 ====> y+1 = . y(x+1)=5/18 ====> x+1 = . ====> (x+1)*(y+1) = . = = now replace xy in the denominator by , and you will get = = .

Solved.