QJEEM22Ma4347: JEE Main 2022 Mathematics - Class 12 JEEM22Ma4347 Solution: If the system of linear equations 2x + y z = 7 x 3y + 2z = 1 x…

Question

Verified Solution • 2025–26 Session moderate

If the system of linear equations

2x + y $-$ z = 7

x $-$ 3y + 2z = 1

x + 4y + $\delta$ z = k, where $\delta$ , k $\in$ R has infinitely many solutions, then $\delta$ + k is equal to:

Accepted Answer

$2x + y - z = 7$

$x - 3y + 2z = 1$

$x + 4y + \delta z = k$

$Δ = | \begin{matrix} 2 & 1 & - 1 \\ 1 & - 3 & 2 \\ 1 & 4 & δ \end{matrix} | = - 7 δ - 21 = 0$

$\delta = - 3$

$Δ_{1} = | \begin{matrix} 7 & 1 & - 1 \\ 1 & - 3 & 2 \\ k & 4 & - 3 \end{matrix} |$

$\Rightarrow 6 - k = 0 \Rightarrow k = 6$

$\delta + k = - 3 + 6 = 3$

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