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Remember that a typical solution
to a system is a point like
(-2,
3)
where the two lines intersect.
But, sometimes this doesn't happen!
Let's graph these two lines:
What's the solution? They
have to intersect to get a solution. But, that's never going
to happen since these lines are parallel. So, there is no
(x,
y)
that is going to work in both equations.
When you are solving by
elimination or substitution, you'll be going about your work...
without a care in the world... and something freaky is going
to happen! You're going to get a false statement like
Something like this is sure to
produce a sick stomach during a test! But, not to worry.
You won't panic, because you'll know what this means. It just
means that the two lines don't intersect.
For the official
answer, you'll want to write something like this:
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These
lines are parallel.
There is no solution. |
TRY IT:
Solve by either
elimination or substitution. Then, check your
answer by graphing:
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