How do you identify if the system 3x-2y=43x2y=4 and 9x-6y=19x6y=1 is consistent or inconsistent?

1 Answer
Jan 2, 2015

Your system is inconsistent:
You can immediately guess that considering that the coefficients of xx and yy of your two equations are multiples. The coefficients of the second are the coefficients of the first multiplied by 33.
This tells you that your equations represent 2 parallel lines (they have the same slope but different yy intercepts).

You can also check by isolating yy from the first:
y=3/2x-2y=32x2
and substituting in the second:
9x-6(3/2x-2)=19x6(32x2)=1 which gives you:
12=112=1 which is false.
Your equations do not share a common solution!

Graphically:
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