Hello from MrBillDoesMath!
Answer: NO points of intersection. The two lines are parallel
Discussion:
Rewrite the equations so the variables and constants line up vertically
x - 2y + 8 = 0
x - 2y -6 = 0 (I added "x" to both sides of the second equation)
Subtract the bottom equation from the the top one:
(x - 2y + 8) - ( x - 2y -6) = 0 or
x - 2y + 8 - x + 2y + 6 = 0 or
(x-x) + (-2y +2y) + (8 + 6) = 0 or
0 + 0 + 14 = 0
14 = 0 !
No solution exists. (Another approach: What is the slope of each line? Hint: 1/2. Since the slopes are the same the lines are parallel and have no points of intersection)
Thank you,
MrB