For which of the following ordered pairs (mu, | vedclass

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(D) The system of equations is given by:$(i) x + 2y + 3z = 1$$(ii) 3x + 4y + 5z = \mu$$(iii) 4x + 4y + 4z = \delta$To check for inconsistency,we perfo

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$(4, 3)$

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(D) The system of equations is given by:$(i) x + 2y + 3z = 1$$(ii) 3x + 4y + 5z = \mu$$(iii) 4x + 4y + 4z = \delta$To check for inconsistency,we perform row operations or eliminate variables.Subtracting $(i)$ from $(ii)$ gives: $(3x-x) + (4y-2y) + (5z-3z) = \mu - 1 \Rightarrow 2x + 2y + 2z = \mu - 1$.Multiplying this by $2$ gives: $4x + 4y + 4z = 2(\mu - 1)$.Comparing this with equation $(iii)$,we have $4x + 4y + 4z = \delta$.For the system to be inconsistent,the left-hand sides must be equal while the right-hand sides are unequal,or the equations must lead to a contradiction like $0 = k$ (where $k 
eq 0$).Thus,if $\delta 
eq 2(\mu - 1)$,the system is inconsistent.Checking the options:For $(A) (1, 0): \delta = 0, 2(\mu - 1) = 2(1 - 1) = 0$. Here $\delta = 2(\mu - 1)$,so it is consistent.For $(B) (4, 6): \delta = 6, 2(\mu - 1) = 2(4 - 1) = 6$. Here $\delta = 2(\mu - 1)$,so it is consistent.For $(C) (3, 4): \delta = 4, 2(\mu - 1) = 2(3 - 1) = 4$. Here $\delta = 2(\mu - 1)$,so it is consistent.For $(D) (4, 3): \delta = 3, 2(\mu - 1) = 2(4 - 1) = 6$. Here $\delta 
eq 2(\mu - 1)$,so the system is inconsistent.

For which of the following ordered pairs $(\mu, \delta)$ is the system of linear equations $x+2y+3z=1$,$3x+4y+5z=\mu$,and $4x+4y+4z=\delta$ inconsistent?

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