How do I use simultaneous equations to solve for the point of intersection for lines.

Question

-y+1=x and y-1=x

Answer 1

-y+1=x ----> x + y = 1
y-1=x -----> x - y = -1
add them
2x = 0
x = 0

sub that into x+y = 1
0+y = 1
y = 1

so they intersect at (0,1)