8TH GRADEMATH 8 IIS – TEST REVIEW NAME: _______________________________ Explain or demonstrate how you would identify the slope of each of the lines below. 1. 4x + 5y = 5. 2. -x + 4y = 16 3. Graph and identify the x-intercept (as an ordered pair) of 4x + 5y = 40. 4. Graph and identify the x-intercept (as an ordered pair) of 9x + 6y = 18 5. The sophomore class holds a car wash to raise money. A local merchant donates all of the supplies. A wash costs $5 per car and $6.50 per van or truck Let x represent the number of cars. Let y represent the number of vans or trucks. a. Write and graph an equation relating x and y to the goal of raising $130.00 b. Tell three combinations of x and y that are solutions to the equation you wrote for the previous question. 6. The student council is sponsoring a carnival to raise money. Tickets cost $5 for adults and $3 for students. Let x represent the number of adults. Let y represent the number of students. a. Write and graph an equation relating x and y to the goal of raising $150.00 b. Tell three combinations of x and y that are solutions to the equation you wrote for the previous question. a. Write an equation to model the total number of boxes sold. b. Write an equation to model the total amount of money raised. boxes of jelly candies 7. Mary has sold 13 boxes of candy for her class fundraiser. She has sold boxes of chocolate for $5 and boxes of fruit jelly candies for $4. Mary has sold $60 worth of candy. c. What is the solution to this system? ________ boxes of chocolate and ________ boxes of jelly candies. boxes of chocolate 8. Rosie has sold 30 flowers for her class fundraiser. She has sold roses for $4 and carnations for $2. Rosie has sold $80 worth of flowers. a. Write an equation to model the total number of flowers sold. b. Write an equation to model the total amount of money raised. c. What is the solution to this system? ________ # of roses and ________ # of carnations. Solve by Substitution. 9. y = 22x + 4 -14x + y = 28 10. y = 25x + 4 -11x + y = 32 11. 22x + y = 4 -14x + y = 60 12. -25x + y = 4 -7x + y = 40 Solve each system below by addition or subtraction. 13. x + 2y = 7 3x – 2y = -3 15. 2x + 2y = 24 2x + 3y = 31 14. 3x + 2y = 14 3x – 3y = -6 16. x + 2y = 5 3x – 2y = 7 17. Consider the system x + 2y = 10 and 2x + 4y = 10. Will this system have one solution, no solutions or infinitely many solutions? Explain how you know, including calculations or diagrams to illustrate your explanation. 18. Consider the system y = 3x + 4 and -12x + 4y = 16. Will this system have one solution, no solutions or infinitely many solutions? Explain how you know, including calculations or diagrams to illustrate your explanation. 19. Consider the system 3x + 4y = 12 and 2x + 4y = 8. Will this system have one solution, no solutions or infinitely many solutions? Explain how you know, including calculations or diagrams to illustrate your explanation. 20. Farmer Fred has a combination of 22 pigs and chickens, and no other animals. Pigs, of course, have 4 legs and chickens have two legs. Somehow the pigs and chickens have gotten into the same pen and all Farmer Fred can see are 62 legs. Help Farmer Fred sort out his animals. How many chickens does he have and how many pigs? Explain or show your work. You can solve this problem by any method you like but no points will be earned for guess and check. 21. The state fair is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 8 vans and 8 buses with 240 students. High School B rented and filled 4 vans and 1 bus with 54 students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus. Explain or show your work. You can solve this problem by any method you like but no points will be earned for guess and check.