4x – 5y = 14 .............eq 1   ---->-5y=-4x+14--->y=(4/5)x-14/5

-12x + 15y = -42..........eq 2   ---->15y=12x-42--->y=(4/5)x-14/5

:

using elimination: multiply eq 1 by 3 and add the two equations together

:

 12x-15y=42.......eq 1 revised

-12x+15y=-42.....eq 2

:

All terms will be eliminated in this system.  In this case one can see that eq 2 is just eq 1 multiplied by -1......therefore these are the same exact lines

:

hence this system has infinite solutions

 

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