Mathematics What should not be the value of k for the pair of equations 2x+3y−5=0   and kx−6y−8=0   to have unique solution.

 What should not be the value of k for the pair of equations 2x+3y5=0   and kx6y8=0   to have unique solution.


  1. A
    1
  2. B
    -2
  3. C
    3
  4. D
    -4 

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    Solution:

    Given pair of linear equations are 2x+3y5=0   and kx6y8=0  . We need to find what value should k not have, so that the given equations have unique solution.
    A system of linear equations a 1 x+ b 1 y+ c 1 =0   and a 2 x+ b 2 y+ c 2 =0   will have unique solutions when a 1 a 2 b 1 b 2  .
    Now from equations 2x+3y5=0   and kx6y8=0  , we have,
    a 1 =2, b 1 =3, c 1 =5   and a 2 =k, b 2 =6, c 2 =8  
    Now, equation the values in the condition, we have,
    2 k 3 6 2(6)3(k) 123k k 12 3 k4  
    Thus, the value of k should not be -4 for the equations to have unique solution.
    Therefore, option 4 is correct.
     
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