The system 3x + ky = 33 and x - y = 4 has solution (7, 3). What is the value of k?

The solution $(7, 3)$ must satisfy both equations. The second checks out: $7 - 3 = 4$. Substitute into the first: $3(7) + k(3) = 33$, so $21 + 3k = 33$, then $3k = 12$ and $k = 4$. A common wrong answer is 12, which is the value of $3k$, one step short. Another is 11, from dividing 33 by 3 and ignoring the $3x$ term. A third is 7, the $x$-value. Always substitute into the equation that contains the unknown, then divide by its coefficient to isolate $k$.