SAT Math practice problem about seating arrangements that seems impossible! Can anybody offer any insight?

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A teacher is figuring out seating charts. If she assigns 2 people/table, she needs 4 extra tables. If she assigns 4 people/table, she has 4 empty tables. how many students are there in the class?

This was all the information I was given on the practice test and it was on the no-calculator version. Unfortunately, this was a secured exam so my instructor couldn't show me the answer key or help me in any way on it, only tell me if I got it right or wrong.

How would you guys do this?

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Let $T$ be the number of tables and $P$ be the number of students. The statement

If she assigns 2 people/table, she needs 4 extra tables.

Translates to the relationship $$ \frac{P}{2} = T + 4$$

The statement

If she assigns 4 people/table, she has 4 empty tables.

Translates to $$ \frac{P}{4} = T -4$$

This gives of a system of two equation and two variables. Can you solve the problem from here?