The system 3x + ky = 21 and x + y = 7 has solution (4, 3). What is the value of k?

The solution $(4, 3)$ satisfies both equations. Check the second: $4 + 3 = 7$. Now substitute into the first equation: $3(4) + k(3) = 21$, so $12 + 3k = 21$, then $3k = 9$ and $k = 3$, choice C. Choice A (7) is the right side of the second equation. Choice B (4) is the $x$-value of the solution. Choice D (9) is the value of $3k$, which is one step short of the answer. Substitute the point into the equation that contains $k$, and then isolate $k$ by dividing by its coefficient.