Question 1194180
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If 5x-y is divisible by 4, then it's also divisible by 2 since 4 = 2*2


Put another way:
4 is a factor of 5x-y
5x-y = 4k for some integer k 
5x-y = 2*(2k)
This shows that 5x-y is even


5x-y is even while 2x+3y is odd
(5x-y)+(2x+3y) = (5x+2x) + (-y+3y) = 7x+2y


We've summed an even number (5x-y) with an odd number (2x+3y) to get an odd result (7x+2y). This concludes the proof.


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Here's a side proof showing that odd+even = odd
This is something for another page (perhaps a reference page in your notebook somewhere).


k = some integer
2k = some even integer
2m+1 = some odd integer


odd+even = (2m+1)+2k = (2m+2k)+1 = 2(m+k)+1 = some other odd integer


This concludes the proof that odd+even = odd
Since order doesn't matter when it comes to adding, it's the same as saying even+odd = odd


Some numeric examples to partially verify the claim:
3+2 = 5
7+14 = 21
19+18 = 37
These are examples to help see why the proof works. Of course you'd need the proof above to fully confirm the claim. 
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