Word Problems
Solve by Graphing
Solve by Substitution
Solve by Elimination
Wild Card
100
Cell Phone Plan A charges $10 for each GB of data, plus $20 for the line fee. Cell Phone Plan B charges $15 for each GB of data, plus $25 for the line fee. Write a system of equations for this situation. Will the services ever charge the same amount? If so, when? 
What is y = 10x + 20 and y = 15x + 25, and NO?
100
By graphing, the solution to the system y = x, y = -x.
What is (0,0)?
100
By substitution, the solution to the system x + y = 2, y = 3.
What is (-1,3)?
100
By elimination, the solution to the system x + 5y = 12, -x +y = 0.
What is (2,2)?
100
Two parallel lines, or a solution similar to 3 = 4, means a system has this type of solution.
What is, NO SOLUTION?
200
Four times one number minus 3 times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers. Hint: use the equations 4x - 3y = 12 and 2x + 3y = 6.
What are 3 and 0?
200
By graphing, the solution to the system y = 3x - 4, y = -3x + 2.
What is (1,-1)?
200
By substitution, the solution to the system 2y - x = 4, and x = 0.
What is (0,2)?
200
By elimination, the solution to the system -4x - 2y = -12, 4x + 8y = -24.
What is (6,-6)?
200
(0,-4) is the solution to the system y = -20x + 1, 20x + y = 6. (What is TRUE? or What is FALSE?)
What is FALSE?
300

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? Hint: use the equations x + y = 13 and 2x + 4y = 40.

What is 6 chickens and 7 pigs?
300
By graphing, the solution to the system y = (1/3)x + 2, y = -x - 2.
What is (-3,1)?
300
By substitution, the solution to the system y = 6x - 11, -2x - 3y = -7.
What is (2,1)?
300
By elimination, the solution to the system 5x + y = 9, 10x - 7y = -18.
What is (1,4)?
300
Two equations that represent the same line, or an equation solution that comes out similar to 3 = 3, means that the system has the following type of solution.
What is INFINITE SOLUTIONS?
400
Two hot air balloons are in the air. Balloon 1 is 10 meters above the ground, rising 15 meters per minute. Balloon 2 is 150 meters above the ground, and is falling 20 meters per minute. When will the balloons be at the same height?
What is 3 weeks?
400
By graphing, the solution to the system x + y = 2 and 2y - x = 10.
What is (-2, 4)?
400
By substitution, the solution to the system -3x + 3y = 4, -x + y = 3.
What is no solution?
400
By elimination, the solution to the system -4x + 9y = 9, x = 3y - 6.
What is (9,5)?
400
The graph of a ONE SOLUTION problem might look like this.
(Graph of 2 parallel lines)
500
The difference of two numbers is 3. Their sum is 13. What are the two numbers?
5 and 8
500
By graphing, the solution to the system 2x + 3y = -17 and y = x - 4.
What is (-1, -5)?
500
By substitution, the solution to the system -5x - 8y = 17, 2x - 7y = -17.
What is (-5,1)?
500
By elimination, the solution to the system 2x + 8y = 6, -5x - 20y = -15.
What is infinite number of solutions?
500

Define a system of equations and define solution.

A system of equations is two or more lines.

A solution is the point of intersection of the lines in the system.

Do not give the points unless that is what they said above. 

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