The 6th grade class is selling raffle tickets at a price of $6 for 5 tickets. Some students may use diagrams with shapes to represent the
situation. For example, here is a diagram representing 10 tickets for $12.
Price in Dollars
12
Number of Tickets
Drawing so many shapes becomes impractical. Double number line
diagrams are easier to work with. The one below represents the price in
dollars for different numbers of raffle tickets all sold at the same rate of
$12 for 10 tickets.
6
12
0
+
18
+
Price in Dollars
Number of Tickets +
0
5
10
15
Here is a task to try with your student.
Raffle tickets cost $6 for 5 tickets.
1. How many tickets can you get for $90?
2. What is the price of 1 ticket?

Asystem of linear equations with more equations than unknowns is sometimes called an overdetermined system. can such a system be consistent? illustrate your answer with a specific system of three equations in two unknowns. choose the correct answer below. a. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 6 b. no, overdetermined systems cannot be consistent because there are fewer free variables than equations. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 12 c. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 8 d. no, overdetermined systems cannot be consistent because there are no free variables. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 24