If the system of linear equations x+ay+z=3 x+2y+2z=6 x+5y+3z=b has no solution, then:
A
a=−1,b≠9
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B
a=1,b≠9
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C
a=−1,b=9
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D
a≠−1,b=9
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Solution
The correct option is Aa=−1,b≠9 For given system of linear equations which has no solution, Case 1: △=0 ∣∣
∣∣1a1122153∣∣
∣∣=0 ⇒1(6−10)−a(3−2)+1(5−2)=0 ⇒a=−1
Case 2: △1≠0 ∣∣
∣∣1−1312615b∣∣
∣∣≠0 ⇒1(2b−30)+1(b−6)+3(5−2)≠0 ⇒b≠9 Hence, a=−1,b≠9