Unit 15/16 Review Solve the system algebraically 1.) 3x – 3y + z = -­‐9 2.) 6x – y = 1 3.) 4x – 2y -­‐ 3z = -­‐1 -­‐4x – 3y – z = 0 2x + 3y + 2z = 9 -­‐4x + y + 2z = 2 2x – y + 2z = 4 -­‐4x + 2y + z = 2 3x + y + z = -­‐7 Identify if the system is independent, dependent, or inconsistent. 4.) x – 5 = -­‐ y 5.) x + y + z = 0 6.) 5x + 4y – z = 1 2y – 10 = -­‐2x 2x + 3y + 2z = -­‐1 2x – 2y + z = 1 x – y + z = 2 -­‐x – y + z = 2 Solve the system using inverse matrix equations. 7.) 2x – y + 2z = 10 8.) x – y + z = 6 9.) 6x – 4y + 5z = 31 4x + 2y – 5z = 10 2x + 3y + 2z = 2 5x + 2y + 2z = 13 x – 3y + 5z = 8 3x + 5y + 4z = 4 x + y + z = 2 Solve the nonlinear systems. (Solve 10 by hand and 11 by graphing calculator.) 10.) y = x2 – 7x – 6 11.) y = x2 –x – 18 y = 8 – 2x y = 2x + 3 12.) Three multiplied by the first number is equal to the second number plus 4. The second number is equal to one plus two multiplied by the third number. The third number is one less than the first number. What is the sum of all three numbers? 13.) You have 17 coins in pennies, nickels, and dimes in your pocket. The value of the coins is $0.47. There are four times the number of pennies as nickels. How many of each type of coin do you have? Perform the indicated operations. 4 −5 1
−7 −10 4
4 7
−9 3
14.) −
15.) 10 7
+
17
0
3 4
−2 1
6 0
−2 −6 1
21 −9 −6
2 6 −1 5
16.) 1 0 3 1