Expert: Abe Mantell - 8/16/2011

Question
elimination method: after you multiply first equation to get one of the variable alike to the second equation and they cancel each other out that's good, but if both variables cancel each out out is that considered no solution or infinite solution?
4x + 5y = 2
8x + 10y = 4
multiply by 2
makes everything alike..
infinite or no solution?

Answer
Hello Diana,

If the two equations turn out to be the same (after multiply or dividing by the
appropriate constants for the elimination process), then that means the two lines
are the same...which means they overlap.  Since two lines which are the same intsect
at infinitely many points (all points on the lines!), that means there are infinitely
many solutions.

Suppose however, you get something like this:
4x + 5y = 2
8x + 10y = 5

Multiplying the 1st equation by 2, gives:
8x + 10y = 4

then when you subtract it from the 2nd one, we get
0=1, which is impossible!  That means the two lines are parallel and do
not intersect.  Hence, no solution.

OK?

Abe