Choice B is the correct answer. To verify if $(5, 4)$ is a solution, we substitute $x = 5$ and $y = 4$ into both equations.

First equation: $x + 3y = 17$$5 + 3(4) = 5 + 12 = 17$ ✓ (True)

Second equation: $2x - y = 6$$2(5) - 4 = 10 - 4 = 6$ ✓ (True)

Since the point satisfies both equations, it is a solution to the system.

💡 Strategic Tip: A solution must work for every equation in the system simultaneously.

Choice A is incorrect because we can always determine if a point is a solution through substitution.

Choice C is incorrect because the point does satisfy both equations.

Choice D is incorrect because the point satisfies both equations, not just the first.