How do you identify if the system #3x-2y=4# and #9x-6y=1# is consistent or inconsistent?

1 Answer
Gió
Jan 2, 2015

Your system is inconsistent:
You can immediately guess that considering that the coefficients of #x# and #y# of your two equations are multiples. The coefficients of the second are the coefficients of the first multiplied by #3#.
This tells you that your equations represent 2 parallel lines (they have the same slope but different #y# intercepts).

You can also check by isolating #y# from the first:
#y=3/2x-2#
and substituting in the second:
#9x-6(3/2x-2)=1# which gives you:
#12=1# which is false.
Your equations do not share a common solution!

Graphically:
enter image source here

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