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Two linear simultaneous equations

3 exam-style questions. Answers and the mark for each step are on the last page.

  1. Question 1Non-calculator · 3 marks

    Solve the simultaneous equations x+y=10x + y = 10 and x−y=4x - y = 4.

    (a) Find the values of xx and yy. Give your answer as (x,y)(x, y). (3)

  2. Question 2Non-calculator · 4 marks

    The sum of two numbers is 23. Three times the larger number minus twice the smaller number is 39.

    (a) Find the two numbers. Give your answer as (larger, smaller). (3)

    (b) Explain how to check your answer. (1)

  3. Question 3Calculator · 3 marks

    (a) Four pens and three notebooks cost £17.40. Two pens and five notebooks cost £21.30. Each pen has the same price and each notebook has the same price. Find the price of one notebook. (3)

Answers and marks

Question 1

(a) x=7x = 7, y=3y = 3

  • M1 Adding the equations to get 2x=142x = 14 (or another correct elimination).
  • A1 The correct answer, x=7x = 7.
  • A1 The correct answer, y=3y = 3.

Question 2

(a) (17,6)(17,6)

  • P1 Write an equation for each statement.
  • P1 Eliminate one letter, for example by substituting y = 23 - x.
  • A1 Correct answer: (17,6)(17,6)

(b) Substitute into both statements: 17 + 6 = 23 and 3 × 17 - 2 × 6 = 51 - 12 = 39.

  • C1 Correct conclusion with supporting reasoning: Substitute into both statements: 17 + 6 = 23 and 3 × 17 - 2 × 6 = 51 - 12 = 39.

Question 3

(a) £3.63.6

  • P1 Establishing 4p+10b=42.64p+10b=42.6 or an equivalent valid method.
  • P1 Establishing 7b=25.27b=25.2 or an equivalent valid method.
  • A1 Correct answer: £3.63.6

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Two linear simultaneous equations

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