Practice Exam 1

Please work out each of the given problems.  Credit will be based on the steps that you show towards the final answer.  Show your work.

Printable Key

Problem 1  Use the method of elimination to solve the system.  Then graph the system to check your solution.

  1.  -3x + 2y = 6
      9x - 6y  =  36
    Solution

  2. 5x + 3y  =  15
    3x - 2y  =       28
    Solution      

 

Problem 2  Use the method of substitution to solve the system.  Then graph the system to check your solution.

  1. 7x + y  =  3
    4x + 3y  =  -8
     Solution

  2. y  =  3x - 2
    6x - 2y  =  4
    Solution

 

Problem 3  Last year, you inherited $30,000 from a distant relative.  You took the money and invested some of it in a bank account that paid 2% interest and invested the rest in stocks that increased 6%.  The total earnings on the invested money was $900.  How much money was invested in the bank account and how much was invested in the stock market?  Show the equations that you set up and how you either used substitution or elimination to solve the system.

Solution

Problem 4  You own a non-profit theater that has 2,000 seats.  In order to break on even Saturday's concert you must collect a total of $24,000 from the ticket sales.  You have decided to partition the theater's seats into "premium seats" which you will sell for $30 per seat and "general admission" seats which you will sell for $10 per seat.  If you are certain the tickets will sell out, how many seats should you sell as "premium seats"?  Show the equations that you set up and how you either used substitution or elimination to solve the system.

Solution

Problem 5  Graph the system of inequalities below.

        3x + 5y < 15
         y > 2x + 1

Solution

Problem 6  

Consider the system of inequalities below.

        y > -1
        x + y < 4
        x - y < 3

Write the coordinates of the plotted points below that are solutions of this system.

       

Solution

Problem 7  Factor

        15x2y3 - 18xy4 + 21x4y2

Solution

Problem 8  Factor 

        6x2 + 9x - 10x -15

Solution

Problem 9  Factor

        x2 - x - 6

Solution

Problem 10  Solve

        6x2 + x - 15  =  0

Solution