Set up a linear system and solve for the following problems:
1. The sum of two integers is 41 and their difference is 5. Find the integers.
2. The sum of two integers is 74. The larger is 13 less than twice the smaller. Find the two integers.
3. A $5,000 principal is invested in two accounts, one earning 1% interest and another earning 6% interest. If the total interest for the year is $170, then how much is invested in each account?
4. A cash register contains $10 bills and $50 bills with a total value of $1080. If there are 28 bills total, then how many of each does the register contain?
5. Pens are sold in a local store for 80 cents each. The factory has $1200 in fixed costs plus 5 cents of additional expense for each pen made. Assuming all pens manufactured can be sold, find the break-even point.