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Question

The value of 'a' for which the system of equations (a+1)3x+(a+2)3y=(a+3)3, (a+1)x+(a+2)y=a+3 ,x+y=1 is consistent ,is

A
-2
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B
-1
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C
1
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D
2
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Solution

The correct option is A -2
For consistent systems
∣ ∣ ∣(a+1)3(a+2)3(a+3)3a+1a+2a+3111∣ ∣ ∣=0
(a+1)3(1)(a+2)3(2)+(a+3)3(1)=0
(a+2)3(a+1)3+(a+2)3(a+3)3=0
(1)(3a2+9a+7)+(1)(3a2+15a+19)=0
6a12=0
a=2

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