Final answer:
Lines 2 and 5, when written in slope-intercept form, have identical slopes but different y-intercepts which makes them parallel. Parallel lines never intersect, thus the system of equations composed of these two lines has no solution.
Step-by-step explanation:
To determine which two lines from the given list create a system of equations with no solution, we must find the ones that have identical slopes but different y-intercepts. Lines with these characteristics are parallel and will never intersect.
Line 1 is y = -2x + 9 and Line 3 is y = 2x + 1. Comparing their slopes, we see that these slopes are different, so these two lines could intersect and thus could have a solution. Therefore, neither of these can be a part of a pair of lines that would not intersect.
Line 2 is in standard form, so let's rearrange it into slope-intercept form to make it easier to compare by isolating y:
3x - 2y = 6
-2y = -3x + 6
y = (3/2)x - 3
Line 4 needs similar rearrangement:
4x + 2y = 2
2y = -4x + 2
y = -2x + 1
Lastly, Line 5 is y = (3/2)x - 3. Comparing Line 2 in its rearranged form with Line 5, we can see they both have the same slope of (3/2), but different y-intercepts. This means they are parallel lines, and so, they will never intersect.
Therefore, Lines 2 and 5 are the two lines from the given list that if used to create a system of equations would have no solution.