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Honors Advanced Algebra with Trigonometry Note Sheet for Homework Name #1 _________ Solve the system of equations. 4x + 2y = 12 5x + 3y = 12 4x + 5y - 2z = -7 -4x + y + z = -2 x - y + 3z = 11 #4 • • • • Date #2 Solve by graphing. #3 #5 Define the variable Set up a system of equations Solve Answer the problem One group of customers at a snack bar bought 8 cheeseburgers, 6 orders of fries, and 6 drinks for a total of $26.10. Another group bought 10 cheeseburgers, 6 orders of fries, and 8 drinks for a total of $31.30. A third group bought 3 cheeseburgers, 2 orders of fries, and 4 drinks for a total of $10.95. Find the price of each item. • • • • Define the variable Set up a system of equations Solve Answer the problem A restaurant manager wants to purchase 200 sets of dishes. One design costs $25 per set and another design costs $45 per set. Her total budget for buying dishes is $7400. How many sets of each design should she purchase? Homework #5: Worksheet Name_________________________ Homework (HAAw/trig) #5 Date___________Period__________ 1-2 Solve each system using substitution. 1. y = 6 - 2x y - 4x = 12 2. y = 9x 6x - y = -2 4. 2x - 4y = 2 x + 2y = -7 3-4 Solve each system using elimination. 3. 4x - y = 6 2x + y = -3 5-8 Solve each system using substitution or elimination (your choice). 5. 1 x + 3y = 9 2 1 x - 4y = -5 2 6. 1 3 x - y = -5 3 2 € € x + 2y = 11 € € 7. 1 x + 2y = 1 2 1 x - y = 11 2 8. x=6- 1 y 2 x - 2y = 16 € € € 9-10 Solve the following application problems using a system of equations. Be sure to represent the unknown (3 variables), set up a system of 3 equations, solve, and answer the problem. 9. The sum of three integers is 39. Twice the smallest integer decreased by 1 equals the largest integer. The middle number increased by 4 equals the largest also. Find all three integers. Define the variable 10. answer The perimeter of a triangle is 40 inches. Twice the smallest side increased by 1 equals the largest side. Two less than the largest side equals the middle-sized side. Find all three sides. Define the variable 11. set up system of eqns / solve set up system of eqns / solve Solve for x, y, and z: x + y + z = 15 x + z = 12 y + z = 10 answer 12-13 Solve by graphing. Be sure to name at least 2 points on each line and use a straight edge. 12. € y= 2 x+5 3 3 y = − x + 18 2 € 13. 4x + 7y = 18 6x - 3y = 0 14-16 Use the set of data to answer the following problems. Cable TV Subscribers 1980 1985 1990 1995 2000 x = Year y = Millions of Subscribers 17.5 35.4 50.5 14. 60.6 66.3 Find the linear regression equation to show how the year and the number of subscribers are related. (Round to the nearest hundredth.) 14.____________________ 15. Graph the scatter plot and the linear regression line on the graph below. Name 2 points on the line whose x-values are 1975 and 2005. Use a straight edge. y 70 Millions of Subscribers 60 50 40 30 20 10 1975 1980 1985 1990 1995 2000 2005 x Year 16. Based on the linear regression equation, how many cable subscribers will there be in 2015? (Round to the nearest hundredth.) 16.____________________ Solutions #5 Homework 2 , 6) 3 Solutions 3. ( 1 , -4) 2 4. (-3, -2) 7. (10, -2) 8. (8, -4) 11. (5, 3, 7) 1. (-1, 8) 2. ( 5. (6, 2) 6. (3, 4) 9. (17, 13, 9) 10. 8 inches, 15 inches, 17 inches 12. (6, 9) 13. (1, 2) 16. 107.46 million subscribers 14. y = 2.46x - 4841.38 15. y (2005, 82.9) 70 Millions of Subscribers 60 50 40 30 20 10 (1975, 9.22) 1975 1980 1985 1990 Year 1995 2000 2005 x