Set 2: Systems of Equations (Advanced)

Choice D is correct. Choice D is the correct answer. Step 1: Divide the first equation by 5: $$\frac{10 x - 15 y}{5} = \frac{20}{5}2x - 3 y = 4$$$ This is exactly the second equation! Conclusion: The lines are identical (coincident) This means infinitely many solutions—every point on one line is also on the other. Strategic Tip: Identical lines are also called "coincident lines" or "the same line." Choice A is incorrect because intersecting at one point requires different slopes. Choice B is incorrect because parallel but not identical would give no solution (different constants). Choice C is incorrect because both lines have slope \frac{2}{3}$, not perpendicular slopes.