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The system of equations 2x+y+z=a,  x2y+z=b,   x+y2z=c is consistent if

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a
a+b+c=0
b
a+b+c≤0
c
a+b+c≠0
d
a+b+c≥0

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detailed solution

Correct option is A

We have Δ= -2111-2111-2=-24-1-1-2-1+11+2=0 ∴For consistency we must have Δ1=Δ2=Δ3=0 ⇒a11b-21c1-2=0 ⇒a4-1-1-2b-c+1b+2c=0 ⇒3a+b+c=0 ⇒a+b+c=0


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