Choice A is the correct answer. Let's substitute $(1, 7)$ into both equations.

First equation: $5x + 2y = 19$$5(1) + 2(7) = 5 + 14 = 19$ ✓

Second equation: $3x - y = -4$$3(1) - 7 = 3 - 7 = -4$ ✓

Since $(1, 7)$ satisfies both equations, it is the Choice B is incorrect because the point satisfies both equations.

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

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