The system 4x + ky = 48 and 2x - y = 8 has solution (6, 4). What is the value of k?

The solution $(6, 4)$ must satisfy both equations. Check the second: $2(6) - 4 = 8$. Substitute into the first: $4(6) + k(4) = 48$, so $24 + 4k = 48$, then $4k = 24$ and $k = 6$. A common wrong answer is 24, which is the value of $4k$ and not $k$. Another is 12, from $\frac{48}{4}$, which ignores the $4x$ term. A third is 4, the value of $y$. Always substitute into the equation that includes the unknown, then divide by its coefficient.