QJEEM21Mae94d: JEE Main 2021 Mathematics - Class 12 JEEM21Mae94d Solution: The values of λ and μ such that the system of equations x + y + …

Question

Verified Solution • 2025–26 Session moderate

The values of

λ

and

μ

such that the system of equations

x + y + z = 6

,

3 x + 5 y + 5 z = 26

,

x + 2 y + λ z = μ

has no solution, are :

Accepted Answer

x + y + z = 6

..... (i)

3 x + 5 y + 5 z = 26

.... (ii)

x + 2 y + λ z = μ

..... (iii)

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

∴

from (i) and (iii)

y + z = 4

..... (iv)

2 y + λ z = μ - 2

.....(v)

(v) - 2 \times (i v)

\Rightarrow (λ - 2) z = μ - 10

\Rightarrow z = \frac{μ - 10}{λ - 2}

&

y = 4 - \frac{μ - 10}{λ - 2}

∴

For no solution

λ

= 2 and

μ

\neq

10.

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