4x·y=10x·y would imply that 4=10 (a false statement) if the dot symbol represents multiplication.
If it represents proportionality as in 4x:y=10x:y, then 4x/y=10x/y, 4=10 (false).
4x·y=10 makes sense, but simply relates x and y and can be reduced to 2x·y=5. This means that y is inversely proportional to x: as x increases y decreases, y=5/(2x). For example, when x=½, y=5, and when x=5, y=½.
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