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Q.

Choose the correct answer:


The system 3x−5y=20 6x−10y=40   is:


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a

Unique solution

b

No solution

c

Infinite many solution

d

none of the above 

answer is C.

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Detailed Solution

The correct answer is option 3.
In the system: a 1 x+ b 1 y+ c 1 =0 a 2 x+ b 2 y+ c 2 =0  
The ratios of coefficients:
x= a 1 a 2 ,y= b 1 b 2 ,z= c 1 c 2  
We get infinite solutions when
a 1 a 1 = b 1 b 1 = c 1 c 1  
Using the equations:
3x−5y=20 ⇒2x−5y−20=0....(1) 6x−10y=40 ⇒6x−10y−40=0......(2)  
Ratios of coefficients:
⇒ a 1 a 2 = 3 6 = 1 2 ⇒ b `1 b 2 = −5 −10 = 1 2 ⇒ c 1 c 2 = 20 40 = 1 2  
Therefore,
a 1 a 1 = b 1 b 1 = c 1 c 1  
There are infinite many solutions to the equation.
 
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