Determining number of solutions to linear equations

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  1. \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: System of linear equations
    There are 3 cases to consider:
    Graphs of system of linear equations with different number of solutions
  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
    1. 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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      Topic Notes
      Depending on whether and how the linear equations in a system touch each other, there will be different number of solutions to the system. There can be one solution, no solution and even infinite solution.