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Question

If the system of linear equations
2x+2y+3z=a
3xy+5z=b
x3y+2z=c
where a, b, c are non-zero real numbers, has more than one solution, then:

A
b+ca=0
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B
bc+a=0
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C
bca=0
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D
a+b+c=0
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Solution

The correct option is C bca=0
Since, system of linear equations has more than one solution
Δ1=0=Δ2=0=Δ3
Δ1=∣ ∣22a31b13c∣ ∣=0
2(c+3b)2(3cb)+a(9+1)=0
8c+8b8a=0
bca=0

Alternate approach:––––––––––––––––––––
Adding first and third equation, we get second equation.
Hence, a+c=b or bca=0

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