We want to check how many intersections line A and B have, that is, we want to check how many common solutions do these equations have:
i) 2x + 2y = 8
ii) x + y = 4
use equation ii) to write y in terms of x as : y=4-x,
substitute y =4-x in equation i):
2x + 2y = 8
2x + 2(4-x) = 8
2x+8-2x=8
8=8
this is always true, which means the equations have infinitely many common solutions.
Answer: There are infinitely many solutions.
