Math 9 · Unit 4: Equations and inequalities · Cambridge Lower Secondary Maths Stage 9

Questions

1. 1. Copy and complete the workings to solve the simultaneous equations y = 2x − 1 and y = x + 5 by the method of substitution.

   Fill the blanks with these.

   • 5
   • 11
   • 13
   • 12
   • 6
   • 1
   • 4
   Check

2. 2. Copy and complete the workings to solve the simultaneous equations y = 6x + 3 and y = 2x − 9.

   Fill the blanks with these.

   • -15
   • -12
   • 4
   • 3
   • 18
   • -6
   • -18
   • 2
   • -3
   Check

3. 3. Copy and complete the table of values for each equation.

   Fill the blanks with these.

   • 4
   • 6
   • 3
   • 8
   • 9
   • 1
   • 10
   • 7
   • 5
   Check

4. 4. The lines y = 2x + 1 and y = x + 4 cross. Where?

   • (3, 7)
   • (1, 3)
   • (7, 3)
   • (0, 4)
   Check

5. 5. Copy and complete the workings to solve the simultaneous equations y = 2x + 1 and y = x + 4 algebraically.

   Fill the blanks with these.

   • 6
   • 3
   • 7
   • 1
   • 8
   • x
   • 5
   • 4
   Check

6. 6. Do the graph (part c) and the algebraic method (part d) give the same solution to y = 2x + 1 and y = x + 4?

   • Yes
   • No
   Check

7. 7. Copy and complete the workings to solve these simultaneous equations using the method of elimination. x + y = 10 and x − y = 4

   Fill the blanks with these.

   • 3
   • 7
   • 10
   • 14
   • 6
   • 4
   Check

8. 8. Copy and complete the workings to solve these simultaneous equations using the method of elimination. x + 5y = 28 and x + 3y = 18

   Fill the blanks with these.

   • 3
   • 25
   • 20
   • 15
   • 10
   • 5
   • 8
   Check

9. 9. Copy and complete the workings to solve these simultaneous equations using the method of elimination. 3x + 2y = 34 and x − 2y = 6

   Fill the blanks with these.

   • 10
   • 34
   • 20
   • 4
   • 6
   • 30
   • 40
   • 2
   Check

10. 10. Solve y = 3x and y = x + 12.

    • x = 4, y = 12
    • x = 3, y = 9
    • x = 6, y = 12
    • x = 6, y = 18
    Check

11. 11. Solve y = 2x + 1 and y = −2x + 9.

    • x = 5, y = 2
    • x = 2, y = 3
    • x = 2, y = 5
    • x = −2, y = 5
    Check

12. 12. Solve y = 3 − x and y = 2x − 15.

    • x = 4, y = −1
    • x = 6, y = 3
    • x = 6, y = −3
    • x = −6, y = 9
    Check

13. 13. Solve y = 4x − 3 and y = x + 3.

    • x = 5, y = 2
    • x = 0, y = 3
    • x = 2, y = 11
    • x = 2, y = 5
    Check

14. 14. Do the graphical method and the algebraic method give the same solution to y = 4x − 3 and y = x + 3?

    • Yes
    • No
    Check

15. 15. Which method is better for an exact answer, the graphical or the algebraic method?

    • The graphical method
    • The algebraic method
    • Neither is ever exact
    • Both are always exact
    Check

16. 16. Solve x + y = 20 and x − y = 16.

    • x = 36, y = −16
    • x = 2, y = 18
    • x = 18, y = 2
    • x = 16, y = 4
    Check

17. 17. Solve 3x + y = 30 and 2x − y = 15.

    • x = 15, y = −15
    • x = 3, y = 9
    • x = 9, y = −3
    • x = 9, y = 3
    Check

18. 18. Solve x + 2y = 21 and 3x − 2y = 15.

    • x = 9, y = 3
    • x = 9, y = 6
    • x = 6, y = 9
    • x = 12, y = 4.5
    Check

19. 19. Solve 3x + 2y = 64 and x + 2y = 40.

    • x = 12, y = 14
    • x = 12, y = 28
    • x = 14, y = 12
    • x = 24, y = 8
    Check

20. 20. Solve x = y − 10 and y = 2x.

    • x = 10, y = 20
    • x = 20, y = 10
    • x = −10, y = −20
    • x = 5, y = 10
    Check