MathematicsState whether the given statement is true/false.The following pair of equations is consistent with unique solution. 6x−3y =11 12x+6y =22  

State whether the given statement is true/false.


The following pair of equations is consistent with unique solution.


6x3y =11 12x+6y =22  


  1. A
    True 
  2. B
    False  

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    Solution:

    Given that the following pairs of linear equations 6x3y=11   and 12x+6y=22   are consistent with unique solution. We need to find whether the given statement is true or false.
    A system of linear equations a 1 x+ b 1 y+ c 1 =0   and a 2 x+ b 2 y+ c 2 =0   is consistent with unique solution when a 1 a 2 b 1 b 2  .
    From equations 6x3y=11   and 12x+6y=22  , we have,
    a 1 =6, b 1 =3, c 1 =11   and a 2 =12, b 2 =6, c 2 =22  
    Now, we have,
    a 1 a 2 = 1 2   and b 1 b 2 = 1 2  
    Hence, we can observe that,
    a 1 a 2 b 1 b 2  
    Thus, the given pair of equation are consistent with unique solutions.
    Therefore, the given statement in the question is true.
    Therefore, option 1 is the correct choice.
     
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