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

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

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

 4 Solve and check this system algebraically:     4m - n + p = 25     3m - 3n + 4p = -23      m + 2n - 3p = 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 3x3 system, find the quadratic function y = Ax2 + 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.