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

We have  Δ= -2111-2111-2=-24-1-1-2-1+11+2=0The system of equation is inconsistent if  −2      1          −a1          −2      −b1           1            −c≠0⇒-2[2c+b]-1[-c+b]-a(3)≠0⇒-4c-2b+c-b-3a≠0⇒-3[a+b+c]≠0⇒a+b+c≠0


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