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Grade 10 · Exponents, Equations and Inequalities
Simultaneous Linear Equations (Grade 10)
MEMORANDUM
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Mark
  / 24

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

  1. 1
    Solve: y = 2x and x + y = 9
    (3)
    x + 2x = 9 → x = 3, y = 6 → (3 ; 6)✓✓✓ (3)
  2. 2
    Solve: y = x + 4 and y = 2x + 1
    (3)
    x + 4 = 2x + 1 → x = 3, y = 7✓✓✓ (3)
  3. 3
    Solve: x + y = 10 and x − y = 2
    (3)
    Add: 2x = 12 → x = 6, y = 4✓✓✓ (3)
  4. 4
    Solve: 2x + y = 7 and 3x − y = 8
    (3)
    Add: 5x = 15 → x = 3, y = 1✓✓✓ (3)
  5. 5
    Solve: 3x + 2y = 12 and x − 2y = 4
    (3)
    Add: 4x = 16 → x = 4, y = 0✓✓✓ (3)
  6. 6
    Solve: 2x + 3y = 13 and 4x − y = 5
    (4)
    x = 2, y = 3✓✓✓✓ (4)
  7. 7
    What does the solution represent graphically?
    (1)
    The point where the two lines cross.✓ (1)
  8. 8
    Three apples and two pears cost R16; one apple and one pear cost R6. Find each price.
    (4)
    3a + 2p = 16, a + p = 6 → apple R4, pear R2✓✓✓✓ (4)
TOTAL: 24 marks
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