Choice A is the correct answer. Let's analyze each system:

System I: $y = 2x + 3$ and $y = 2x - 1$

• Same slope (2), different y-intercepts (3 and -1)
• Parallel lines → No solution ✓

System II: $y = 2x + 3$ and $y = -2x + 3$

• Different slopes (2 and -2)
• Intersecting lines → One solution

System III: $y = 2x + 3$ and $2y = 4x + 6$

• Divide second by 2: $y = 2x + 3$
• Same line → Infinitely many solutions

Conclusion: Only System I has no solution.

💡 Strategic Tip:

• Same slope, different intercepts → No solution
• Different slopes → One solution
• Same equation → Infinitely many solutions

Choice B is incorrect because System II has one solution (lines intersect).

Choice C is incorrect because System III has infinitely many solutions (same line).

Choice D is incorrect because System II has one solution.