Applications of Systems
Solve Systems by Graphing
Solve Systems by Substitution
Solve Systems by Elimination
Check the solution!
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!

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