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100
There are 13 animals in the barn. Some are chickens and some are pigs. There are 40 legs in all. How many chickens and how many pigs are there?
6 chickens and 7 pigs
100

y = x

y = -x

(0,0)

100

x + y = 2 

y = 3

(-1, 3)

100

x + 5y = 12 

-x + y = 0

(2, 2)

100

Is (4,5) the solution to the following system? 

4x - y = 12 

x + 6y = 13

NO!

200
The sum of two numbers is 12. Their difference is 4. What are the two numbers?
The two numbers are 8 and 4.
200

y = 3x - 4

y = -3x + 2

(1,-1)

200

x = 2y - 4

10y - x = 20

(0, 2)

200

-4x - 2y = -12 

4x + 8y = -24

(6, -6)

200

Is (0,-4) the solution to the system? 

y = -20x + 1 

20x + y = 6

NO!

300
There are 200 vehicles in a parking lot. Some are cars and some are motorcycles. There are 698 wheels total. How many cars and how many motorcycles are there?
51 motorcycles and 149 cars
300

2x + y = 4

y = -x +3

(1,2)

300

y = 6x - 11 

-2x - 3y = -7

(2, 1)

300

5x + y = 9 

10x - 7y = -18

(1, 4)

300

Is (-2, 1) the solution to the system? 

6x - 3y = -15 

2x + y = -3

YES!

400
Harold sells small cups of lemonade for $1 and large cups for $3. Harold sold a total of 155 cups of lemonade and collected a total of $235. How many small cups and how many large cups did Harold sell?
115 small cups and 40 large cups of lemonade.
400

2x +2y = 4 

y= -3x +4

(1,1)

400

-2x + 3y = 4 

y = x + 3

(-5, -2)

400

-4x + 9y = 9 

-3y + x = - 6

(9, 5)

400

TRUE or FALSE: This system has NO SOLUTION. 

y = 3x + 4 

y = -x - 4

FALSE!

500
A group of 75 teachers and students went to a museum. Teacher tickets cost $10 and student tickets cost $7. The whole group paid a total of $552. How many teachers and how many students went to the museum?
9 teachers and 66 students.
500

3x + 3y =9

-x + y = 5

(-1,4)

500

y - 10 = -7x

3x + 2y = 9

(1,3)

500

2x + 8y = 6 

-5x - 16y = -15

(3, 0)

500

Is (-3,-1) the solution to this system? 

y=(4/3)x + 3 

(2/3)x + y = -3

YES!