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Year 6 · Maths · Algebra and sequences · Lesson 5

Equations with two unknowns

Find pairs of whole numbers that satisfy equations with two unknowns, work systematically, and use a second fact to find a single solution.

Whiteboard video lesson: Equations with two unknowns

22-minute video lesson

Teaching, worked examples and 20 practice questions solved step by step.

Watch free for a month

What your child will learn

  • Find pairs that satisfy an equation
  • Work systematically
  • Use conditions
  • Solve with two facts
  • Solve word problems

The method

  1. Start with the smallest value.
  2. Work out the other letter.
  3. Go up one at a time.
  4. Use extra facts to choose.

Key words: unknown, pair, systematic, equation, solution.

Worked examples

The first three practice questions from the lesson, with every step.

Question 1

a and b are whole numbers. a + b = 5. Find all the possible pairs.

  1. Step 1: Try a = 1: then b = 4
  2. Step 2: Make a table, trying each value of a
  3. Step 3: (a, b): (1, 4), (2, 3), (3, 2), (4, 1)

Answer: (a, b): (1, 4), (2, 3), (3, 2), (4, 1)

Question 2

a and b are whole numbers. a + b = 8. Find all the possible pairs.

  1. Step 1: Try a = 1: then b = 7
  2. Step 2: Make a table, trying each value of a
  3. Step 3: (a, b): (1, 7), (2, 6), (3, 5), (4, 4), (5, 3), (6, 2), (7, 1)

Answer: (a, b): (1, 7), (2, 6), (3, 5), (4, 4), (5, 3), (6, 2), (7, 1)

Question 3

a and b are whole numbers less than 9. a − b = 3. Find all the possible pairs.

  1. Step 1: Try a = 4: then b = 1
  2. Step 2: Make a table, trying each value of a
  3. Step 3: (a, b): (4, 1), (5, 2), (6, 3), (7, 4), (8, 5)

Answer: (a, b): (4, 1), (5, 2), (6, 3), (7, 4), (8, 5)