Question 23716
If you just add these two equations together, you will subtract out the x terms AND the y terms:

3x - 4y = 9
-3x + 4y = 12


0 + 0 = 21

Obviously this is NOT possible.  There is NO way that 0 = 21!  At least not in OUR lifetime!!  This means that there is NO SOLUTION.  Some textbooks will call this the Empty Set, and they write this either with empty set braces: {  }, or with the Greek letter "phi" which is a 0 with a slash:  {{{ phi }}}.  I personally think this is very confusing to students, so I prefer to just call  it NO SOLUTION.


Now, think about what situtation could happen with equations of two straight lines that would cause a NO SOLUTION situation.  What happened is that the lines are PARALLEL!!


R^2 at SCC