Write and Solve Systems of Equations Practice — Grade 8 math

Lesson 6-5: Write and Solve Systems of Equations — Practice Questions

1. Which method is most efficient for solving the system of equations $y = -3x + 5$ and $y = x - 3$?
- A. Graphing
- B. Substitution
- C. Elimination
- D. All are equally efficient
2. What is the most efficient method to solve the system of equations $x = 4y - 1$ and $2x + 3y = 11$?
- A. Graphing
- B. Substitution
- C. Elimination
- D. None of these
3. For the system $4x - 5y = 8$ and $-4x + 3y = -4$, which solving method is most efficient?
- A. Graphing
- B. Substitution
- C. Elimination
- D. All are equally efficient
4. Which method is generally most efficient for solving the system with equations $y - 2x = 5$ and $3x + 4y = 10$?
- A. Graphing
- B. Substitution
- C. Elimination
- D. None of these
5. Identify the most efficient method for solving the system of equations $2x + 7y = 3$ and $5x - 3y = 22$.
- A. Graphing
- B. Substitution
- C. Elimination
- D. All are equally efficient
6. The sum of two numbers is 40. One number is 8 less than the other. What is the larger number? ___
7. Gym A charges a 50 dollar fee plus 20 dollars per month. Gym B charges 30 dollars per month. After how many months is the total cost for both gyms the same?
- A. 2
- B. 5
- C. 8
- D. 10
8. The perimeter of a rectangular garden is 60 feet. The length is 6 feet more than the width. What is the length of the garden in feet? ___
9. A theater sold 150 tickets. Adult tickets cost 12 dollars and child tickets 8 dollars. Revenue was 1560 dollars. Let 'a' be adult tickets and 'c' be child tickets. Which system models this?
- A. $a + c = 150$ and $12a + 8c = 1560$
- B. $a + c = 1560$ and $12a + 8c = 150$
- C. $a - c = 150$ and $12a - 8c = 1560$
- D. $a + c = 150$ and $20(a+c) = 1560$
10. The perimeter of a rectangular field is 100 meters. Its length is 10 meters less than three times its width. What is the width of the field in meters? ___