Joe is opening an educational fund for his son who needs to go to graduate school for $2$ years from now. Joe has the money to invest in two different funds, A and B$,$ now. The first fund $($A$)$ matures every year with a rate of return of $4\%.$ The second fund $($B$)$ matures every $2$ years with a rate of return of $9\%.$ His son requires $$19,000$ for each of the $3$ years that he is in graduate school. Joe wants to invest in the funds and pay the required education expenses from the amount maturing from the prior investments. Let A$1$ be the amount of money invested in fund A for the first year, B$1$ be the amount of money invested in fund B for the first year, and so on$.$