Set 6: Systems of Equations (Intermediate)

Choice C is correct. Choice C is the correct answer. Step 1: Multiply the first equation by 2: $$2(2 x - 3 y) = 2(6)4x - 6 y = 12$$$ This is exactly the second equation! Step 2: Since both equations represent the same line, they are identical (coincident). This means infinitely many solutions—every point on the line satisfies both equations. Strategic Tip: Identical lines are a special case of "infinitely many solutions." Choice A is incorrect because intersecting at one point requires different slopes. Choice B is incorrect because perpendicular lines have slopes whose product is -1$. Here, both have slope$\frac{2}{3}$. Choice D is incorrect because the lines are not just parallel—they're the same line.