A bank wants us to build an ATM for which there are three limitations$.$ First one is that number of bank notes must be $97,$ being of $10,20$ and $m.$ Second one is that the total amount must be $1330.$ And third one is that the number of $10$ notes must be double than the number of $20$ ones.

a$)$ Found a system of equations to check, using it$,$ if ATM is doable. Explain your answer.

b$)$ Explain if ATM can have $100$ notes.