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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