1. How can you determine whether a system has no solution by graphing?
2. Solve by graphing:
3. Solve by the substitution method. Determine whether the equations are independent, dependent, or inconsistent.
4. Ticket sales. Tickets for a concert were sold to adults for $3 and to students for $2. If the total receipts were $824 and twice as many adult tickets as student tickets were sold, then how many of each were sold?
5. What are we trying to accomplish by adding the equations?
6. Solve by the addition method:
7. Solve by the addition method:
x/3-y/2 = -5/6
x/5-y/3 = -3/5
8. Books and magazines. At Gwen's garage sale, all books were one price, and all magazines were another price. Harriet bought four books and three magazines for $1.45, and June bought two books and five magazines for $1.25. What was the price of a book and what was the price of a magazine?
9. How are the planes positioned when a system of linear equations in three variables is independent?
3x+y-z = 2
2x-y = -8
y+3z = 22
x-z = -8
4x-2y-2z = 5
2x-y-z = 7
-4x+2y+2z = 6
This solution is comprised of detailed explanation and step-by-step calculation of the given problems and provides students with a clear perspective of the underlying concepts.