Question

if 10x = 10x
are there any real solutions?
or are all real numbers a solution?

Answer 1

all real numbers are solutions.

for two linear equations of 1 variable y = f(x) your options are always:

no solution [lines never intersect]
one solution [lines intersect; straight lines, so once]
infinitely many solutions [ lines are parallel/on top of each other ]

the line 10x and 10x are parallel

Answer 2

Thanks! That's what I thought it was!