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

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

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Answer 1 · 2015-01-02T01:06:10

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

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

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

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