The system 2x + ky = 14 and x - y = 1 has solution (5, 4). What is the value of k?

The solution $(5, 4)$ must satisfy both equations. Check the second: $5 - 4 = 1$, which works. Substitute into the first: $2(5) + k(4) = 14$, so $10 + 4k = 14$, then $4k = 4$ and $k = 1$, choice A. Choice B (2) gives $10 + 8 = 18$, not 14. Choice C (3) gives $10 + 12 = 22$. Choice D (7) comes from $14 \div 2$ and gives $10 + 28 = 38$. Substitute the given point into the equation that contains $k$ and solve.