
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 + 2 b  c = 4
a + b + c = 3
2 a + b + c = 5



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



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



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



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 3 x3 system, find the quadratic function y = Ax^{2} + Bx + C whose graph passes through the points (2,7), (3,1), and (4,9).



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.



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