Determining number of solutions to linear equations

Lessons

• Introduction
  $\bullet$ The solutions to a system of equations are the points of intersection of the graphs.
  $\bullet$ For a system consisting of two linear equations:
  There are 3 cases to consider:
  
  

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• 1.
  State whether each of the following systems have ONE, NONE, or INFINITE solutions
  
  i) 3x + y = 7
  4x + y = 7
  
  ii) 6x + 2y = 10
  3x + y = 5
  
  iii) x - y = 3
  3x - 3y = 6
  

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• 2.
  Find a value for c that will give the following system:
  

  3y + 2cx = 6
  

  y - 6x = 0
  
  i) one solution
  
  ii) no solutions
  

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