If the system of linear equations 2 x+y-z=7x-3 y+2 z=1 ; x+4 y+ z=k where , k ∈ ℝ has infinitely many solutions, then +k is equal to:

Correct answer: B. 3 For getting infinite solutions D=0, D_1=D_2=D=0 then check all the three equations Let Δ=| array ccc 2 & 1 & -1 1 & -3 & 2 1 & 4 & array |=0 =-3 And Δ_1=| array ccc 7 & 1 & -1 1 & -3 & 2 k & 4 & -3 array |=0 k=6 +k=3

BITSAT 2024Paper 1

Exam: BITSAT
Year: 2024
Paper: Paper 1
Subject: Mathematics
Chapter: Determinants

BITSAT 2024 · Paper 1 · Mathematics · Determinants

If the system of linear equations 2 x+y-z=7x-3 y+2 z=1 ; x+4 y+ z=k...

If the system of linear equations

2 x+y-z=7x-3 y+2 z=1 ; x+4 y+\delta z=k

where

\delta, k \in \mathbb{R}

has infinitely many solutions, then

\delta+k

is equal to:

Options

A $-3$
B $3$
C $6$
D $9$

Correct answer

B. $3$

Step-by-step solution

For getting infinite solutions

\mathrm{D}=0, \mathrm{D}_1=\mathrm{D}_2=\mathrm{D}=0

then check all the three equations Let

\Delta=\left|

\begin{array}{ccc}2 & 1 & -1 \\ 1 & -3 & 2 \\ 1 & 4 & \delta\end{array}

\right|=0 \quad \Rightarrow \delta=-3

And

\Delta_1=\left|

\begin{array}{ccc}7 & 1 & -1 \\ 1 & -3 & 2 \\ k & 4 & -3\end{array}

\right|=0 \Rightarrow k=6\Rightarrow \delta+k=3

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