Practice Page

Directions: Grab paper and pencil. The SOLUTION will show only one possible solution method. The algebraic solutions will show the "elimination" method of solution.

1.
Solve and check this system algebraically:
    a + 2b - c = 4
    a + b + c = 3
    2a + b + c = 5

3by3guy

 

 

2.
Solve and check this system algebraically:
    3x - y + 4z = -5
    6x - y + 3z = -9
    5x + 5y - 5z = 20

3by3guy

 

 

3.
Solve and check this system algebraically:
    4x - 2y + 2z = 8
    -x + 3y - z = 5
    2x - y + z = 4

3by3guy

 

 

4.
Solve and check this system algebraically:
    4m - n + p = 25
    3m - 3n + 4p = -23
     m + 2n - 3p = 25

3by3guy

 

 

5.
A piggy bank contains only nickels, dimes and quarters. Given the following information, use a 3x3 system to determine how many of each type of coin are in the bank.
• The coins total $4.50.
• There are 32 coins in the bank.
• The number of nickels and dimes together is 8 more than the number of quarters.

 


6.
Using a 3x3 system, find the quadratic function y = Ax2 + Bx + C whose graph passes through the points (2,-7), (3,-1), and (4,9).

quadpic1

 

 

7.
Using a 3x3 system, determine three numbers that satisfy the following conditions:
• the sum of the three numbers is 2.
• the sum of the first number, 5 times the second number, and 5 times the third number is -10.
• the sum of the first number, double the second number, and triple the third number is -3.

 

 

8.
Caleb placed $5,500 in three investments that pay an annual interest of 4%, 5% and 7%. He placed twice as much money in the 7% investment as he did in the 4% investment. His total interest for the year is $320. Using a 3x3 system, determine the amount of money Caleb placed in each of the three investments.

caleb2



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