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

Related questions
See all questions in Consistent and Inconsistent Linear Systems
Impact of this question
4271 views around the world
You can reuse this answer
Creative Commons License