For which of the following ordered pairs (μ, ), the system of...

D = \left|\begin{cases}3 & 4 & 5 \\ 1 & 2 & 3 \\ 4 & 4 & 4\end{cases}\right|\left({R}_{3} \to {R}_{3} - 2{R}_{1} + 3{R}_{2}\right)
= \left|\begin{cases}3 & 4 & 5 \\ 1 & 2 & 3 \\ 0 & 0 & 0\end{cases}\right| = 0
Now, let ${P}_{3} ≡ 4x + 4y + 4z - \delta = 0 .$ If the system has solutions it will have infinite solution, so,${P}_{3} ≡ \alpha{P}_{1} + \beta{P}_{2}$
Hence, $3\alpha + \beta = 4$ and $4\alpha + 2\beta = 4 ⇒ \alpha = 2and\beta = - 2$
So, for infinite solution $2\mu - 2 = \delta$

For system to be inconsistent,

$2\mu \ne \delta + 2$
So, checking option, $( 4, 3 )$ satisfies.