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 $(k+1)x+(2k-1)y=7$ $(2k+1)x+(k+5)y=10$ has :

Question

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

$(k+1)x+(2k-1)y=7$

$(2k+1)x+(k+5)y=10$

has :

unique solution satisfying $x-y=1$

infinitely many solutions

no solution

unique solution satisfying $x+y=1$

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