systems_of_equations_practice_test

Systems of Equations Practice Test Overview

• The practice test contains 20 questions.

• Focuses on various methods to solve systems of equations:

  • Graphing

  • Substitution

  • Elimination

• Some questions include graphs for better visualization.

Problems Overview

Page 1 Questions

1. Graphing Method:

   • Solve the system:

     • Equation 1: y = 2x - 3

     • Equation 2: y = -x + 1

2. Substitution Method:

   • Solve the system:

     • Equation 1: x + y = 10

     • Equation 2: y = 2x + 4

3. Elimination Method:

   • Solve the system:

     • Equation 1: 3x + 2y = 12

     • Equation 2: 5x - 2y = 8

4. Number of Solutions:

   • Determine solution type:

     • Equation 1: y = 3x + 1

     • Equation 2: 6x - 2y = -2

5. Substitution Method:

   • Solve the system:

     • Equation 1: y = 4x - 5

     • Equation 2: 2x + y = 7

6. Elimination Method:

   • Solve the system:

     • Equation 1: 2x + 3y = 9

     • Equation 2: 4x + 6y = 18

7. Any Method:

   • Solve the system:

     • Equation 1: x - y = 4

     • Equation 2: x + y = 10

8. Application Problem:

   • Find prices of apples and bananas:

     • Cost Equation 1: 3 apples + 2 bananas = $8

     • Cost Equation 2: 2 apples + 3 bananas = $7

Page 2 Questions

9. Graphing Method:

   • Solve the system:

     • Equation 1: y = -x + 4

     • Equation 2: y = 2x - 1

10. Elimination Method:

    • Solve the system:

      • Equation 1: 5x + 4y = 20

      • Equation 2: 10x + 8y = 40

11. Substitution Method:

    • Solve the system:

      • Equation 1: y = 3x + 2

      • Equation 2: 2x - y = -4

12. Solution Type:

    • Determine if the system has no solution, one solution, or infinitely many solutions:

      • Equation 1: y = -2x + 5

      • Equation 2: 4x + 2y = 10

13. Any Method:

    • Solve the system:

      • Equation 1: 7x - 3y = 5

      • Equation 2: 2x + y = 8

14. Graphing Method:

    • Solve the system:

      • Equation 1: y = x + 2

      • Equation 2: y = -2x + 5

15. Intersection Point:

    • Find the intersection point:

      • Equation 1: y = (1/2)x - 3

      • Equation 2: y = -x + 2

16. Elimination Method:

    • Solve the system:

      • Equation 1: 6x - 5y = 12

      • Equation 2: -3x + 2.5y = -6

17. Substitution Method:

    • Solve the system:

      • Equation 1: y = x - 7

      • Equation 2: 3x + 2y = 4

18. Application Problem:

    • Find number of tickets sold:

      • Cost Equation: 5 adults at $10 + 8 children at $7 = $101.

Page 3 Questions

19. Graphing Method:

    • Solve the system:

      • Equation 1: y = (3/4)x - 2

      • Equation 2: y = -x + 1

20. Elimination Method:

    • Solve the system:

      • Equation 1: 4x + y = 11

      • Equation 2: -8x - 2y = -22