If I ask a girl out and she says she is "busy" doing X. Does this mean "leave me alone" or "keep trying"?

A typical text / phone conversation conversation will proceed as follows:

Me; Hey, I was going to get a drink on Thursday night and I was hoping you could tag along, are you free?

Her: No, I am going over to my parents for dinner. :(. Sorry.

LAME!

furthermore,

1) Is she says she is busy, and doesn't suggest a different day should I give up?

2) If she says she is busy, what is a good followup response, e.g. "What day are you free, maybe our schedules will work out" etc.

I don't speak "woman" and hopefully you all can "translate for me". I realize we are all busy these days but I get this response A LOT, sometimes I succeed with persistence but I'd rather just get her to chase me a little bit ;).
If I ask a girl out and she says she is "busy" doing X. Does this mean "leave me alone" or "keep trying"?
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