SOLUTION: How would I use the method of substitution to solve this problem? -x+2y=2 x-2y=-2

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Question 938281: How would I use the method of substitution to solve this problem?
-x+2y=2
x-2y=-2
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
-x+2y = 2
 x-2y = -2

Solve the second one for x   x-2y = -2
                                x = -2+2y

Substitute (-2+2y) for x in the first one:

      x-2y = -2
(-2+2y)-2y = -2
  -2+2y-2y = -2
        -2 = -2

This equation -2 = -2 is an identity.
When trying to solve using substitution or elimination, if we get an
identity, that means there are infinitely many solutions. The graphs are the
same line.

Answer: There are infinitely many solutions.  This is called
a DEPENDENT SYSTEM.

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[Note: BTW, in other problems when trying to solve using substitution 
or elimination, if we get a contradiction, such as -2 = -1, that means there
are NO solutions. The graphs are parallel lines.  That would be called an
INCONSISTENT SYSTEM.]

Edwin
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