SOLUTION: If 5x-y is divisible by 4 and 2x+3y is odd. Then 7x+2y is odd for all x,y ∈Z.

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Question 1194179: If 5x-y is divisible by 4 and 2x+3y is odd. Then 7x+2y is odd for all x,y ∈Z.
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
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If 5x-y is divisible by 4 and 2x+3y is odd. Then 7x+2y is odd for all x,y ∈Z.
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            To be mathematically correct  (and do not scare readers),  the statement needs to be  modified.
            The modified version is  THIS : 

                If x and y are integer numbers such that 5x-y is divisible by 4 and 2x+3y is odd, then 7x+2y is odd.

            Below is my solution for this modified version. 


Since 2x + 3y is odd, it means that 3y is odd.


In turn, it means that y is odd.


Next, 5x-y is divisible by 4.  It implies that x-y is divisible by 4.

Since y is odd (see above), it means that x is odd.


Then 7x is odd, and hence 7x + 2y is odd.

Proved and solved.