A test has $35$ problems, which are worth a total of $230$ points. There are two types of problems on the test. The multiple-choice problems are worth $5$ points each and the essay questions are worth $10$ points each. Let $m$ represent the number of multiple-choice problems there are on the test and let $e$ represent the number of essay questions there are on the test. Write two equations to make up a system of equations that this situation suggests. (Do not solve the system.)