MathematicsState whether the given statement is true or false.The pair of equations x+3y=6   and x−3y=12   are consistent with unique solutions.

State whether the given statement is true or false.


The pair of equations x+3y=6   and x3y=12   are consistent with unique solutions.


  1. A
    True
  2. B
    False 

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    Solution:

    Given that the following pairs of linear equations x+3y=6   and x3y=12   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+by+ 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 x+3y=6   and x3y=12  , we have,
    a 1 =1, b 1 =3, c 1 =6   and a 2 =1, b 2 =3, c 2 =12  
    Now, we have,
    a 1 a 2 = 1 1 a 1 a 2 =1   And,
    b 1 b 2 = 3 3 b 1 b 2 =1  
    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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