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If the system of equations $x+2 y+3 z=3$ ; $4 x+3 y-4 z=4$ ; $8 x+4 y-\lambda z=9+\mu$ has infinitely many solutions, then the ordered pair $(\lambda, \mu)$ is equal to
$\left(\frac{72}{5}, \frac{21}{5}\right)$
$\left(\frac{-72}{5}, \frac{-21}{5}\right)$
$\left(\frac{72}{5}, \frac{-21}{5}\right)$
$\left(\frac{-72}{5}, \frac{21}{5}\right)$
Solution
$x+2 y+3 z=3$
$4 x+3 y-4 z=4$
$8 x+4 y-\lambda z=9+\mu \quad \ldots \ldots . \text { (iii) }$
$\text { (i) } \times 4-\text { (ii) } \Rightarrow 5 y+16 z=8 \ldots \ldots \text { (iv) }$
$\text { (ii) } \times 2-\text { (iii) } \Rightarrow 2 y+(\lambda-8) z=-1-\mu \ldots \ldots(v)$
$\text { (iv) } \times 2-\text { (iii) } \times 5 \Rightarrow(32-5(\lambda-8)) z=16-5(-1-\mu)$
$\text { For infinite solutions } \Rightarrow 72-5 \lambda=0 \Rightarrow \lambda=\frac{72}{5}$
$21+5 \mu=0 \Rightarrow \mu=\frac{-21}{5}$
$\Rightarrow(\lambda, \mu) \equiv\left(\frac{72}{5}, \frac{-21}{5}\right)$
