Algebra

When equations have infinitely many solutions, How would you know this?
also, when working on equations that has no solutions, How would I know this? If posible can you give me examples of each. Thank you

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asked by Kim
  1. Here is an example of two equations with infinite number of solutions

    x+y=4
    3x+3y=12

    Why infinite? They represent the same line, they share the same set of solutions.

    Here is one that has no solutions.

    y=3x+5
    y=3x+3

    Here, the lines are parallel, they have the same slope, but are offset (different intercepts). Therefore they share no common point (solution).

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