All dishwashers are cold fill & these days most washing machines.
You plumb them in so both have there own supply of the cold water mains.
THe mains pressure will be able to supply both machines, should they both be on at the same time & your cold water will still flow from the tap but at slightly reduced pressure.
A word of warning on the 'Y' connector. My girlfriend had one of those fitted for her dishwasher and washing machine, but it was under stress because the hose was only just long enough. This carried on weeping for many months (probably years) and caused a rot problem as it was unseen.
Do the job properly - it may seem more expensive in the short term, but in practice will work out cheaper.
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