Question

How many solutions exist for the system, x + y = 1 and y = -x + 1? a no solution b one solution c infinitely many solutions

Answer 1

y = -x+1 is in the form y=mx+b. To compare their slopes, let's get x+y=1 into y=mx+b form. 
x+y=1
-x     -x 
-----------
y=-x +1
Both functions have a slope of -1, and both have the y-intercept of 1. 
Since they are the same line, they will be on top of each other and have infinitely many solutions.