Activities

1. Determine whether the line through points (1, 6) and (-5, 1) will intersect the line running through points (3, 4) and (-3, -1).

2. The length of a rectangle is 3 meters more than its width.  The perimeter is 26 meters.  Write a system of equations that could be used to find the dimensions of the rectangle.

3. Miguel cooked 39 hamburgers and hot dogs at a cookout.  He cooked twice as many hot dogs as hamburgers.  Write a system of equations that could be used to find how many hamburgers he cooked.

4. From the school carnival Joe had some 2-point tickets and some 5-point tickets he won from playing the games. He chose a prize worth 96 ticket points. If he had 39 tickets in all, how many 2-point tickets did he have? Write two linear equations in two variables and solve.

5. The cost of 12 donuts and 4 bagels is $13.20.  The cost of 24 donuts and 6 bagels is $24.30.  How much do one donut and one bagel cost?  Write a system of equations and solve.

Answer Key/Rubric

1. No, the two lines are parallel.

2. Acceptable responses may include, but are not limited to:

Let l = length

Let w = width

Equations:

3. Acceptable responses may include, but are not limited to:

Let h = hamburgers

Let d = hotdogs

Equations:

4. Joe had 33 two-point tickets.
   Acceptable work may include, but is not limited to:

(All work should be shown)

Let x = two point tickets

Let y = five point tickets

Equations: 

Solution: 

5. Donuts cost $1.05 each and bagels cost $0.75 each.
   Acceptable answers may include, but are not limited to:

(All work should be shown)

Let d = donuts

Let b = bagels

Equations:

Solution: