Question 5: Tell x, y ⋲ Z. If (5x + 46y) ⋮ 16, then x + 6y is divisible by:

We have:

5x + 46y = 5x + 30y + 16y = (5x + 30y) +16y = 5(x + 6y) + 16y

Since 5x + 46y is divisible by 16 and 16y is divisible by 16, then 5(x+6y) is divisible by 16.

But 5 is not divisible by 16, so x + 6y is divisible by 16

So if 5x + 46y is divisible by 16, then x + 6y is also divisible by 16.