"The values of $\lambda$ and $\mu$ such that the system of equations $x + y + z = 6$, $3x + 5y + 5z = 26$, $x + 2y + \lambda z = \mu$ has no solution, are :"

Question

Accepted Answer

"$x + y + z = 6$ ..... (i)

$3x + 5y + 5z = 26$ .... (ii)

$x + 2y + \lambda z = \mu$ ..... (iii)

$5 \times (i) - (ii) \Rightarrow 2x = 4 \Rightarrow x = 2$

$\therefore$ from (i) and (iii)

$y + z = 4$ ..... (iv)

$2y + \lambda z = \mu - 2$ .....(v)

$(v) - 2 \times (iv)$

$\Rightarrow (\lambda - 2)z = \mu - 10$

$\Rightarrow z = {{\mu - 10} \over {\lambda - 2}}$ & $y = 4 - {{\mu - 10} \over {\lambda - 2}}$

$\therefore$ For no solution $\lambda$ = 2 and $\mu$ $\ne$ 10."

The values of $\lambda$ and $\mu$ such that the system of equations $x + y + z = 6$, $3x + 5y + 5z = 26$, $x + 2y + \lambda z = \mu$ has no solution, are :

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The values of $\lambda$ and $\mu$ such that the system of equations $x + y + z = 6$, $3x + 5y + 5z = 26$, $x + 2y + \lambda z = \mu$ has no solution, are :

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