No Solution or Infinite Solutions

When given a system of equalities, there are 3 possibilities for the solution. No solution, infinite solutions, or exactly one solution. The key is knowing which of the 3 is correct for the system you're working with. 

You know your system has infinite solutions when you get a row of zeroes in your augmented matrix. For example in the picture the 3rd row is all zeroes. 

You know you have a system with no solutions, when you get an impossible equation such as all zeroes in a row except for the last number is not a zero. For example in the picture the second row has all zeroes besides the last number.

For further detail, here is the link to the website. 

http://tutorial.math.lamar.edu/Classes/Alg/AugmentedMatrixII.aspx