Set 17: Systems of Equations (Intermediate)

Choice C is correct. Choice C is the correct answer. To verify if $(1, 8)$ is a solution, we substitute $x = 1$ and $y = 8$ into both equations. First equation: $2x + y = 102(1) + 8 = 2 + 8 = 10$ ✓ (True) Second equation: $5x - y = -35(1) - 8 = 5 - 8 = -3$ ✓ (True) Since the point satisfies both equations, it is a solution to the system. Strategic Tip: A point must satisfy ALL equations in a system to be considered a solution. Choice A is incorrect because the point does satisfy both equations. Choice B is incorrect because the point satisfies both equations, not just the first. Choice D is incorrect because we can always determine if a point is a solution through direct substitution.