If the system of linear equations 2x+2y+3z=a 3x−y+5z=b x−3y+2z=c
where a,b,c are non-zero real numbers, has more than one solution, then:
A
b+c−a=0
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B
b−c+a=0
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C
b−c−a=0
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D
a+b+c=0
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Solution
The correct option is Cb−c−a=0 Since, system of linear equations has more than one solution ∴Δ1=0=Δ2=0=Δ3 Δ1=∣∣
∣∣22a3−1b1−3c∣∣
∣∣=0 ⇒2(−c+3b)−2(3c−b)+a(−9+1)=0 ⇒−8c+8b−8a=0 ⇒b−c−a=0
Alternate approach:––––––––––––––––––––––
Adding first and third equation, we get second equation.
Hence, a+c=b or b−c−a=0