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

Jan 2, 2015

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:
$y = \frac{3}{2} x - 2$
$9 x - 6 \left(\frac{3}{2} x - 2\right) = 1$ which gives you:
$12 = 1$ which is false.