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If the system of equations x+2y3z=1, p+2z=3, 2p+1y+z=2 is consistent, then the value of p=_____________

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a
-2
b
−12
c
0
d
2

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detailed solution

Correct option is A

We have z=3p+2,p+2≠0,p≠-2,p≠-12∣12-300p+202p+11=01[0-(p+2)(2p+1)]-()0+()0=0(p+2)(2p+1)=0⇒p=-2 p=-12But for p=−2the system of equations is Inconsistent


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