Set 9: Systems of Equations (Advanced)

Choice B is correct. Choice B is the correct answer. System I: $y = 3 x + 1$ and $y = 3 x - 2$ - Same slope (3), different y-intercepts - Parallel lines → No solution System II: $y = 3 x + 1$ and $y = -3 x + 1$ - Different slopes (3 and -3) - Intersecting lines → Exactly one solution ✓ System III: $y = 3 x + 1$ and $3y = 9 x + 3$ - Divide second by 3: $y = 3 x + 1$ - Same line → Infinitely many solutions Conclusion: Only System II has exactly one solution. Strategic Tip: Different slopes guarantee exactly one solution (lines must intersect). Choice A is incorrect because System I has no solution (parallel lines). Choice C is incorrect because System III has infinitely many solutions. Choice D is incorrect because System III has infinitely many solutions, not one.