Avoid eating out--with 6 dollars at a fast food restaurant you can make a healthier more satisfying meal from scratch with leftovers for another meal.
Some of the websites suggested are really good.
Pasta and sauce is pretty cheap. A box of pasta--1-2 dollars. A jar of sauce--1 to 2 dollars. So a meal for your family for 4 dollars.
You can also make some pasta, then in a frying pan cook the pasta in some oil (olive oil is best) l and garlic . Then serve topped with fresh tomatoes and parmesan cheese. You can also tossed in leftover chicken, meatball meat, etc. This is a great way to use up leftovers.
If you buy a whole chicken, and cook with rice or potatoes and a veggie that will probably cost about 12-15 dollars and you can easily get 2-3 meals out of it.
With the leftover chicken you can use in the above garlic pasta recipe, or make a chicken caccitore (various ways of making it...simple way is to saute chopped onion and powdered or fresh garlic in a skillet with some olive oil, add the leftover chicken and a can of crushed tomatoes with Italian seasoning and parmesan cheese. Serve over pasta.
When the chicken is almost gone, save the extra chicken and boil the bones to make a broth. You can then make gravy, or save the chicken broth and chicken and make a homemade chicken noodle soup.
Grilled cheese and soup is cheap and easy. A loaf of bread for 4 meals or more--about 2 bucks. Some American cheese for a couple dollars more, and a can of soup you can get for about a dollar, usually they have sales. Easily several meals of grilled cheese and soup for 10 dollars or under.
You can provide some variety with the grilled cheese...add a little
pasta sauce or a slice of tomato and/or some chopped onion
Turkey burger is cheaper than hamburger. You can use either and make a meatloaf (really good if you top with a glaze of ketchup, brown sugar, and a little dijon) or homemade meatballs.
Hope that helps, good luck, I know how you feel. I'm on a tight budget here too...