Set 8: Systems of Equations (Intermediate)

Choice B is correct. Choice B is the correct answer. To verify if $(4, 1)$ is a solution, we substitute $x = 4$ and $y = 1$ into both equations. First equation: $2x + 3 y = 112(4) + 3(1) = 8 + 3 = 11$ ✓ (True) Second equation: $x - 2 y = 2$ $4- 2(1) = 4 - 2 = 2$ ✓ (True) Since the point satisfies both equations, it is a solution to the system. Strategic Tip: A point must satisfy ALL equations to be a solution to the system. Choice A is incorrect because the point satisfies both equations, not just the second one. Choice C is incorrect because the point does satisfy both equations. Choice D is incorrect because we can always determine if a point is a solution through direct substitution.