For a certain value of , the system has no solutions. What is this value of ?\(\begin{align*} x + y + 3z &= 10, \\ 4x + 2y + 5z &= 7, \\ kx + z &= 3 \end{align*}\)

From the first two equations, [3x + 3y + 9z = 37.]Adding this equation to the third equation, we get [4kx + 3y + 10z = 40,]so 4kx−3y=−3. But this equation has no solution, since the left-hand side is a multiple of 4, and the right-hand side is not.