If the system of equations

x+y+z=2

2 x+ | vedclass

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Question

For infinite solutions

$\Delta=\Delta_{ x }=\Delta_{ y }=\Delta_{ z }=0$

Now $\Delta=0 \Rightarrow\left|\begin{array}{ccc}1 & 1 & 1 \ 2

Vedclass · Accepted Answer

$2 \lambda+\mu=14$

Vedclass · Answer

For infinite solutions

$\Delta=\Delta_{ x }=\Delta_{ y }=\Delta_{ z }=0$

Now $\Delta=0 \Rightarrow\left|\begin{array}{ccc}1 & 1 & 1 \ 2 & 4 & -1 \ 3 & 2 & \lambda\end{array}ight|=0$

$\Rightarrow \lambda=\frac{9}{2}$

$\Delta_{x=0} \Rightarrow\left|\begin{array}{ccc}2 & 1 & 1 \ 6 & 4 & -1 \ \mu & 2 & -\frac{9}{2}\end{array}ight|=0$

$\Rightarrow \mu=5$

For $\lambda=\frac{9}{2}\;and\; \mu=5, \Delta_{ y }=\Delta_{ z }=0$

Now check option $2 \lambda+\mu=14$

If the system of equations

$x+y+z=2$

$2 x+4 y-z=6$

$3 x+2 y+\lambda z=\mu$ has infinitely many solutions, then

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