Set 17: Systems of Equations

Choice B is correct. Choice B is the correct answer. System I: $y = 6 x + 2$ and $y = 6 x - 5$ - Same slope (6), different intercepts (2 and -5) - Parallel lines → No solution System II: $y = 6 x + 2$ and $3y = 18 x + 6$ - Divide second by 3: $y = 6 x + 2$ - Same line → Infinitely many solutions ✓ System III: $y = 6 x + 2$ and $y = -6 x + 2$ - Different slopes (6 and -6) - Intersecting lines → One solution Conclusion: Only System II has infinitely many solutions. Strategic Tip: For infinitely many solutions, equations must represent the exact same line (same slope, same intercept). Choice A is incorrect because System I has no solution (parallel lines). Choice C is incorrect because System III has one solution (different slopes). Choice D is incorrect because System I has no solution.