How do you know when an equation has infinitely many solutions?

Question

How do you know when an equation has no solution?

Answer 1

If the variable drops out, and you end up with a true statement, then there is an infinite number so solutions,
if the end statement is false, there is not solution

e.g.

2x - 4 = 2(x-2)
2x-4 = 2x-4
0 = 0 ..... infinite number of solutions

2x-4 = 2(x-5)
2x-4 = 2x-10
-4 = -10 ... false!, no solution

Answer 2

Thank you

Answer 3

X^2+8x+10=0