Applied Practice with
Systems of Linear Equations
Topic Index | Algebra Index | Regents Exam Prep Center

 

Grab your paper, pencil and graphing calculator.  Solve the following problems using either a substitution method, an addition/subtraction method, or a graphical method.
In each problem, set up a system of equations.

 

1. Two small pitchers and one large pitcher can hold 8 cups of water.  One large pitcher minus one small pitcher constitutes 2 cups of water.  How many cups of  water can each pitcher hold?
                                                               

Answer   

 

 

2. A test has twenty questions worth 100 points.  The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each.  How many multiple choice questions are on the test?

Answer   

 

 

3. Margie is responsible for buying a week's supply of food and medication for the dogs and cats at a local shelter.  The food and medication for each dog costs twice as much as those supplies for a cat.  She needs to feed 164 cats and 24 dogs.  Her budget is $4240.  How much can Margie spend on each dog for food and medication?  

Answer   

 

 

4. Bill and Steve decide to spend the afternoon at an amusement park enjoying their favorite activities, the water slide and the gigantic Ferris wheel.  Their tickets are stamped each time they slide or ride.  At the end of the afternoon they have the following tickets:

 Fun Time Amusements

Water Slide:

Ferris Wheel: 

Total:  $17.70

Bill's Ticket

 Fun Time Amusements

Water Slide: 

Ferris Wheel: 

Total:  $15.55

Steve's Ticket

How much does it cost to ride the Ferris Wheel?
How much does it cost to slide on the Water Slide?

Answer   



 

5. The equations 5x + 2y = 48 and 3x + 2y = 32 represent the money collected from school concert tickets sales during two class periods.  If x represents the cost for each adult ticket and y represents the cost for each student ticket, what is the cost for each adult ticket?

Answer