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Word Problems
Solve by Graphing
Solve by Substitution
Solve by Elimination
Is the Solution Correct?
100
There are 13 animals in the barn. Some are chickens and some are pigs. There are 40 legs in all. How many of each animal are there?
What is 6 chickens and 7 pigs?
100

By graphing, the solution to the system 

y = x

y = -x

What is (0,0) ?

100

The solution to the system y =-x+2

y = x +4

What is (-1,3) ?

100

The solution to the system x + 5y = 12 

-x +y = 0

What is (2,2) ?

100

True or False: (4,5) is the solution to the following system? 4x - y = 12 and  x + 6y = 13

Justify your answer.

What is False ?

200
Find the value of two numbers if their sum is 12 and their difference is 4.
What is (8,4) ?
200

By graphing, the solution to the system    y = 3x - 4

y = -3x + 2

What is (1,-1)?

200

y = 1/2x + 4     

y =1/10x + 2

What is (-5,1.5) ?

200

The solution to the system -4x - 2y = -12

4x + 8y = -24

What is (6,-6)?

200

True or False: (0,-4) the solution to the system y = -20x + 1  and 20x + y = 6

Justify your answer

What is False?

300
John went to Yellow Stone National Park one day this summer. All of the people at the park were either hiking or bike riding. There were 178 more hikers than bike riders. If there were a total of 676 people at the park, how many were hiking and how many were riding their bikes?
What is 427 hikers and 249 bikers ?
300

By graphing, the solution to the system

y = (1/3)x + 2

y = -x - 2

What is (-3,1) ?

300

The solution to the system

y = 6x - 11  

-2x - 3y = -7

What is (2,1) ?

300

The solution to the system 5x + y = 9

10x - 7y = -18

What is (1,4)?

300

True or False: (-2,1) is a solution to the system 6x - 3y = -15  and 2x + y = -3

Justify your answer

What is True?

400
Harold had a summer lemonade stand where he sold small cups of lemonade for $1.25 and large cups for $2.50. If Harold sold a total of 155 cups of lemonade and collected a total of $265, how many cups of each type did he sell?
What is 98 small cups and 57 large cups of lemonade?
400

By graphing, the solution to the system      y = -(3/2)x - 4

y = (1/2)x + 4

What is (-4,2) ?

400

The solution to the system y = x + 4  

y= x + 3

What is no solution?

400

The solution to the system -4x + 9y = 9

x = 3y - 6

What is (9,5)?

400

True or False: No solution describes the solution to the following system y = 3x + 4  and y = -x - 4

Justify your answer

What is False?

500
Phil bought 6 new compact disks and 2 used compact disks for $127.92. At the same prices, Mackenzie bought 3 new compact disks and 8 used compact disks for $133.89. Find the cost of buying a single used compact disk.
What is $9.99 ?
500

By graphing, the solution to the system

y = (5/4)x - 2

y = (5/4)x -1

What is no solution?

500

The solution to the system

y = 5/8x - 2 1/8  

2x - 7y = -17

What is (-5,1) ?

500

The solution to the system 2x + 8y = 6

-5x - 20y = -15

What is infinite number of solutions?

500

True or False: (-3,-1) is the solution to y=(4/3)x + 3 & (2/3)x + y = -3

What is (-3,-1)?