A conference event has seating constraints. Room A can seat 3 per table and Room B can seat 5 per table. They must seat at least 100 total people and have at most 30 tables combined. Let a = the tables in Room A, and b = the tables in Room B. Form the system of inequalities and determine one feasible integer solution, $(a,b)$, that will meet both constraints. Show your work.

$(0,20)$ because $5\cdot 20=100$ meets the seating requirement exactly but it violates the table limit stated in the second constraint.

$(30,0)$ because maximizing one room will always meet the seating requirement while minimizing the amount of tables is irrelevant.

$(10,15)$ because $3\left(10\right)+5\left(15\right)=105$ and $10+15=25$ which will actually violate the seating requirement constraint by too much.

$(17,10)$ because $3\left(17\right)+5\left(10\right)=101\ge 100$ and $17+10=27\le 30$, so both constraints will be satisfied.