Question

How many solutions exist for the system, x + y = 1 and y = -x + 1?

Answer 1

y = -x + 1 is the same as y + x = 1, which is clearly the same as x + y = 1 (the first equation you have)

Answer 2

Thus, you can imagine that both lines would in fact be lying directly on top of each other (they are the same line)... so Let me draw this:

Answer 3

touching each other everywhere*, would that be*

Answer 4

yep, the system has infinitely many solutions

Answer 5

Actually it's an identity, not an equation, so there are infinitely many values of x and y.