line a: 2x + 2y = 8 line b: x + y = 4 which statement is true about the solution to the set of equations? it is (8, 4). it is (4, 8). there is no solution. there are infinitely many solutions.

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.

 There are infinitely many solutions.