If the system of equations $\begin{matrix}3x+4y+5z= \mu \\x+2y + 3z=1 \\4x+4y + 4z =\delta \end{matrix}$ is consistent, then $(\delta, \mu )$ can be

(4, 3)

The correct answer is option (3) : (4, 3)

For the given system of equations, we find that

$D= 0, D_1= - 4\mu + 2\delta + 4, D_2= 8 \mu - 4\delta - 8 $

and $D_3=- 4\mu + 2\delta + 8 $

So, the system will be consistent if

$D_1= D_2= D_3= 0 ⇒2\mu = \delta + 2$

Clearly, $\delta = 4, \mu = 3 $ satisfies this equation. Hence, option (3) is correct.