Set 10: Systems of Equations (Intermediate)

Choice A is correct. Choice A is the correct answer. System I: $y = 2 x + 3$ and $y = 2 x - 1$ - Same slope (2), different y-intercepts (3 and -1) - Parallel lines → No solution ✓ System II: $y = 2 x + 3$ and $y = -2 x + 3$ - Different slopes (2 and -2) - Intersecting lines → One solution System III: $y = 2 x + 3$ and $2y = 4 x + 6$ - Divide second by 2: $y = 2 x + 3$ - 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.