2.16 Algebraic solution of linear equations in three unknowns Quiz: AQA Further Maths, Unit 2

The 20 questions

1. How many solutions does a consistent system of three independent linear equations in x, y and z have?

   • Exactly two solutions
   • One unique solution
   • Infinitely many solutions
   • No solutions

2. If x = 1 and y = 2 in x + y + z = 6, what is z?

   • 5
   • 7
   • 9
   • 3

3. Which of these is a linear equation in three unknowns?

   • x + y/z = 2
   • xyz = 1
   • x^2 + y = 3z
   • 2x + 3y − z = 4

4. Which triple satisfies x + y + z = 6 and 2x − y = 0?

   • (2, 1, 3)
   • (3, 1, 2)
   • (1, 2, 4)
   • (1, 2, 3)

5. Solve x + y + z = 6, x − y + z = 2 and x + 2y − z = 3. Which triple is correct?

   • (3/2, 3, 3/2)
   • (1, 2, 3)
   • (2, 2, 2)
   • (3/2, 2, 5/2)

6. Solve 2x + y + z = 7, x − y = 1 and x + z = 4. Which triple is correct?

   • (2, 1, 2)
   • (3, 2, 1)
   • (2, 2, 1)
   • (1, 2, 2)

7. Solve x − y + z = 0, 2x + y − z = 3 and x + 2y + z = 9. Which triple is correct?

   • (3, 1, 2)
   • (1, 3, 2)
   • (1, 2, 3)
   • (2, 3, 1)

8. Given x + y = 5, y + z = 7 and x + z = 6, what is x + y + z?

   • 6
   • 18
   • 12
   • 9

9. Three friends share £12. Amount a = 2b and amount c = b. How much is a?

   • £3
   • £4
   • £9
   • £6

10. Solve x + 2y − z = −3, 3x − y + 2z = 13 and −x + y + z = 0. What is z?

    • −1
    • 5
    • 3
    • 2

11. If x = 2y and z = y + 3 with x + y + z = 15, what is y?

    • 5
    • 4
    • 3
    • 2

12. Solve 2x − 3y + z = 1, x + y − z = 0 and 3x + 2y + 2z = 9. What is z?

    • 3
    • 2
    • 1
    • 0

13. For which k does the system x + y + z = 1, x = y, 2x + z = k have infinitely many solutions?

    • −1
    • 2
    • 1
    • 0

14. Given x + y = 4, y + z = 6 and x + z = 8, what is x?

    • 3
    • 4
    • 1
    • 5

15. Solve x/2 + y = 4, y + z = 5 and x − z = 1. What is y?

    • 1
    • 4
    • 3
    • 2

16. Which equation results from adding x + y + z = 6 and x − z = 2 to eliminate z?

    • x + 2y = 8
    • 2x + y = 8
    • x + y = 4
    • 2x + y + z = 8

17. Given x + y = 3, y + z = 4 and x + z = 5, what is x − y + z?

    • 4
    • 2
    • 6
    • 8

18. Solve 2x + 2y + 2z = 12, x − y = 0 and z = 2x. What is z?

    • 3
    • 2
    • 6
    • 1.5

19. Red sweets are twice blue sweets and green sweets are 6 more than blue. There are 30 sweets in total. How many are green?

    • 12
    • 6
    • 10
    • 18

20. Solve x + y = 7, y + z = 9 and x + z = 8. What is y?

    • 6
    • 5
    • 3
    • 4

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