text: # Equation with Two Variables: How Many Answers? (1)
  
  In this worksheet, students must find how many integer solutions there are to a given equation with two variables.
  
  Key stage:  KS 2
  
  Curriculum topic:   Maths and Numerical Reasoning
  
  Curriculum subtopic:   Equations and Algebra
  
  Difficulty level:
  
  ### QUESTION 1 of 10
  
  In this worksheet, all the answers must be whole positive numbers or zero.
  
  An equation with two variables involves two numbers which must be found.
  
  Look at this equation:
  
  a + b = 8
  
  The two numbers, a and b, must add to 8.
  
  They are whole positive numbers or zero.
  
  What could they be?
  
  If a is 0, b must be 8.
  
  If a is 1, b must be 7.
  
  If a is 2, b must be 6 etc....
  
  The results can be shown in a table:
  
  a   b
  0 8
  1 7
  2 6
  3 5
  4 4
  5 3
  6 2
  7 1
  8 0
  
  There are 9 solutions.
  
  Look at this equation:
  
  a + b = 2
  
  Match the answers for b to the answers for a, to give the correct solutions.
  
  ## Column B
  
  a = 0
  b = 0
  a = 1
  b = 2
  a = 2
  b = 1
  
  Look at this equation:
  
  a + b = 2
  
  How many solutions does it have where a and b are whole numbers or zero?
  
  Look at this equation:
  
  a + b = 3
  
  Match the answers for b to the answers for a, to give the correct solutions.
  
  ## Column B
  
  a = 0
  b = 1
  a = 1
  b = 3
  a = 2
  b = 2
  a = 3
  b = 0
  
  Look at this equation:
  
  a + b = 3
  
  How many solutions does it have where a and b are whole numbers or zero?
  
  Look at this equation:
  
  a + b = 4
  
  Match the answers for b to the answers for a, to give the correct solutions.
  
  ## Column B
  
  a = 0
  b = 4
  a = 1
  b = 3
  a = 2
  b = 2
  a = 3
  b = 0
  a = 4
  b = 1
  
  Look at this equation:
  
  a + b = 4
  
  How many solutions does it have where a and b are whole numbers or zero?
  
  Look at this equation:
  
  a + b = 5
  
  Match the answers for b to the answers for a, to give the correct solutions.
  
  ## Column B
  
  a = 0
  b = 3
  a = 1
  b = 4
  a = 2
  b = 5
  a = 3
  b = 0
  a = 4
  b = 1
  a = 5
  b = 2
  
  Look at this equation:
  
  a + b = 5
  
  How many solutions does it have where a and b are whole numbers or zero?
  
  Look at this equation:
  
  a + b = 7
  
  How many solutions does it have where a and b are whole numbers or zero?
  
  Look at this equation:
  
  a + b = 10
  
  How many solutions does it have where a and b are whole numbers or zero?
  
  • Question 1
  
  Look at this equation:
  
  a + b = 2
  
  Match the answers for b to the answers for a, to give the correct solutions.
  
  ## Column B
  
  a = 0
  b = 2
  a = 1
  b = 1
  a = 2
  b = 0
  EDDIE SAYS
  0 + 2 = 2
  1 + 1 = 2
  2 + 0 = 2
  • Question 2
  
  Look at this equation:
  
  a + b = 2
  
  How many solutions does it have where a and b are whole numbers or zero?
  
  3
  EDDIE SAYS
  0 + 2 = 2
  1 + 1 = 2
  2 + 0 = 2
  • Question 3
  
  Look at this equation:
  
  a + b = 3
  
  Match the answers for b to the answers for a, to give the correct solutions.
  
  ## Column B
  
  a = 0
  b = 3
  a = 1
  b = 2
  a = 2
  b = 1
  a = 3
  b = 0
  EDDIE SAYS
  0 + 3 = 3
  1 + 2 = 3
  2 + 1 = 3
  3 + 0 = 3
  • Question 4
  
  Look at this equation:
  
  a + b = 3
  
  How many solutions does it have where a and b are whole numbers or zero?
  
  4
  EDDIE SAYS
  0 + 3 = 3
  1 + 2 = 3
  2 + 1 = 3
  3 + 0 = 3
  • Question 5
  
  Look at this equation:
  
  a + b = 4
  
  Match the answers for b to the answers for a, to give the correct solutions.
  
  ## Column B
  
  a = 0
  b = 4
  a = 1
  b = 3
  a = 2
  b = 2
  a = 3
  b = 1
  a = 4
  b = 0
  EDDIE SAYS
  0 + 4 = 4
  1 + 3 = 4
  2 + 2 = 4
  3 + 1 = 4
  4 + 0 = 4
  • Question 6
  
  Look at this equation:
  
  a + b = 4
  
  How many solutions does it have where a and b are whole numbers or zero?
  
  5
  EDDIE SAYS
  0 + 4 = 4
  1 + 3 = 4
  2 + 2 = 4
  3 + 1 = 4
  4 + 0 = 4
  • Question 7
  
  Look at this equation:
  
  a + b = 5
  
  Match the answers for b to the answers for a, to give the correct solutions.
  
  ## Column B
  
  a = 0
  b = 5
  a = 1
  b = 4
  a = 2
  b = 3
  a = 3
  b = 2
  a = 4
  b = 1
  a = 5
  b = 0
  EDDIE SAYS
  0 + 5 = 5
  1 + 4 = 5
  2 + 3 = 5
  3 + 2 = 5
  4 + 1 = 5
  5 + 0 = 5
  • Question 8
  
  Look at this equation:
  
  a + b = 5
  
  How many solutions does it have where a and b are whole numbers or zero?
  
  6
  EDDIE SAYS
  0 + 5 = 5
  1 + 4 = 5
  2 + 3 = 5
  3 + 2 = 5
  4 + 1 = 5
  5 + 0 = 5
  • Question 9
  
  Look at this equation:
  
  a + b = 7
  
  How many solutions does it have where a and b are whole numbers or zero?
  
  8
  EDDIE SAYS
  0 + 7 = 7
  1 + 6 = 7
  2 + 5 = 7
  3 + 4 = 7
  4 + 3 = 7
  5 + 2 = 7
  6 + 1 = 7
  7 + 0 = 7
  • Question 10
  
  Look at this equation:
  
  a + b = 10
  
  How many solutions does it have where a and b are whole numbers or zero?
  
  11
  EDDIE SAYS
  0 + 10 = 10
  1 + 9 = 10
  2 + 8 = 10
  3 + 7 = 10
  4 + 6 = 10
  5 + 5 = 10
  6 + 4 = 10
  7 + 3 = 10
  8 + 2 = 10
  9 + 1 = 10
  10 + 0 = 10
  ---- OR ----
  
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