Set 8: Systems of Equations (Advanced)

Choice C is correct. Choice C is the correct answer. To verify if $(6, 3)$ is a solution, we substitute $x = 6$ and $y = 3$ into both equations. First equation: $x - 2 y = 0$ $6- 2(3) = 6 - 6 = 0$ ✓ (True) Second equation: $3x + y = 213(6) + 3 = 18 + 3 = 21$ ✓ (True) Since the point satisfies both equations, it is a solution to the system. Strategic Tip: A point is only a solution if it works for ALL equations in the system. Choice A is incorrect because the point satisfies both equations, not just the first one. Choice B is incorrect because we can always determine if a point is a solution through substitution. Choice D is incorrect because the point does satisfy both equations.