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Word Problems
Solve by Graphing
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, find the solution to the system

y = x

y = -x

What is (0,0) ?

100

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

4x - y = 12 

x + 6y = 13

NO

200

Find the value of two numbers if their sum is 12 and their difference is 4.

What is (8,4) ?

200

By graphing, find the solution to the system

y = 3x - 4

y = - 3x + 2

What is (1,-1)?

200

Is (0,- 4) a solution to the system 

y = - 20x + 1 

20x + y = 6

No

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, find the solution to the system

y = (1/3)x + 2

y = - x - 2

What is (-3,1) ?

300

Is (-2,1) a solution to the system 

6x - 3y = - 15 

2x + y = - 3

Yes

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, find the solution to the system

y = -(3/2)x - 4

y = (1/2)x + 4

What is (-4,2) ?

400

Is there a solution to this system of equations? Why or why not?

y = 3x + 4 

y - 3x = - 4

No, because these lines are parallel

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, find the solution to the system

y = (5/4)x - 2

y = (5/4)x - 1

No solution... parallel lines

500

Is (-3,-1) a solution to 

y=(4/3)x + 3 

(2/3)x + y = -3

Yes