QJEEM18Ma899a: JEE Main 2018 Mathematics - Class 12 JEEM18Ma899a Solution: If the system of linear equations x + ay + z = 3 x + 2y + 2z =…

Question

Verified Solution • 2025–26 Session moderate

If the system of linear equations
x + ay + z = 3
x + 2y + 2z = 6
x + 5y + 3z = b
has no solution, then :

Accepted Answer

As the given system of equations has no solution then

Δ

= 0 and at least one of

Δ

₁,

Δ

₂ and

Δ

₂ should not be zero.

∴

Δ

=

| \begin{matrix} 1 & a & 1 \\ 1 & 2 & 2 \\ 1 & 5 & 3 \end{matrix} | = 0

\Rightarrow

-

a

- 1 = 0

\Rightarrow

a = - 1

Δ

₂ =

| \begin{matrix} 1 & 3 & 1 \\ 1 & 6 & 2 \\ 1 & b & 3 \end{matrix} | \neq 0

\Rightarrow

b

\neq

0

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