The system 5x + ky = 29 and x - y = 1 has solution (3, 2). What is the value of k?

The solution $(3, 2)$ must satisfy both equations. The second checks out: $3 - 2 = 1$. Substitute into the first equation: $5(3) + k(2) = 29$, so $15 + 2k = 29$, then $2k = 14$ and $k = 7$, choice A. Choice B (5) is the coefficient of $x$. Choice C (3) is the $x$-value of the solution. Choice D (9) fails the check: $15 + 18 = 33$, not 29. Check: $5(3) + 7(2) = 15 + 14 = 29$. Substitute the point into the equation that contains the unknown $k$.