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Remember that a typical solution to a system is a point like (-23)where the two lines intersect.

But, sometimes this doesn't happen!

Let's graph these two lines:

x + y = 1

x + y = 4

a graph of the lines x + y = 1 and x + y = 4

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 (xy) 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

0 = 8

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:

These lines are parallel.
There is no solution.

 


TRY IT:

Solve by either elimination or substitution.  Then, check your answer by graphing:

3x - y = 6

6x - 2y = 3