Question

Explain the 2 different answers you can get when solving an equation and the variable is dropped out.

Answer 1

Example:\[\Large\rm y=2x+3\]\[\Large\rm y=2x+2\]Setting these two equations equal to one another,\[\Large\rm 2x+3=2x+2\]Subtracting 2x from each side gives us:\[\Large\rm 3=2\]We know this to be false.
Therefore the system of equations has `no solution`.

Answer 2

I can't think of a good example for the other thing that your'e looking for.
Let's just choose something obvious like a system setup like this:\[\Large\rm y_1=4x+4\]\[\Large\rm y_2=4x+4\]Setting them equal to one another,\[\Large\rm 4x+4=4x+4\]Again we'll subtract 4x from each side,\[\Large\rm 4=4\]Our variable falls out once again.
But the result is true.

This tells us that there are `infinitely many solutions`.
Our x's share every point in common.

Answer 3

So when your variable falls out, just remember that it's telling you something about `every x value`.

Either every point is a solution, or no points are.

Answer 4

ok thank you dood!!!

Answer 5

np \c:/ hope that helps.