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Let the system of linear equations \(x+y+kz=2\) \(2x+3y−z=1\) \(3x+4y+2z=k\) have infinitely many solutions. Then the sy…

Q1

Let the system of linear equations

\(x+y+kz=2\)

\(2x+3y−z=1\)

\(3x+4y+2z=k\)

have infinitely many solutions. Then the system

\((k+1)x+(2k−1)y=7\)

\((2k+1)x+(k+5)y=10\text{ has :}\)

[JEE Main 2023, 30 Jan (Shift 1)]

a

infinitely many solutions

b

unique solution satisfying \(x-y=1\)

c

no solution

d

unique solution satisfying \(x+y=1\)

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