AP EAMCET · Maths · Determinants
The system of equations \(x+y+z=5, x+2 y+a z=9, x+2 y+z=b\) is inconsistent if
- A \(a=1, b=9\)
- B \(a=1, b \neq 9\)
- C \(a \neq 1, b=9\)
- D \(a \neq 1, b \neq 9\)
Answer & Solution
Correct Answer
(B) \(a=1, b \neq 9\)
Step-by-step Solution
Detailed explanation
\((x+2y+az)-(x+y+z) = 9-5 \Rightarrow y+(a-1)z = 4\) \((x+2y+z)-(x+y+z) = b-5 \Rightarrow y = b-5\) \((b-5)+(a-1)z = 4 \Rightarrow (a-1)z = 9-b\) For inconsistency: \(a-1=0\) and \(9-b \neq 0\) \(a=1, b \neq 9\)
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