MathematicsThe pair of equations  kx-4y=3 and 6x-12y=9 have a unique solution when value for k is all real numbers except ____.

The pair of equations  kx-4y=3 and 6x-12y=9 have a unique solution when value for k is all real numbers except ____.


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    Solution:

    The pair of equations  kx-4y=3 and 6x-12y=9 have a unique solution when value for k is all real numbers except 2.
    Given systems of equations are kx-4y=3 and 6x-12y=9.
    A system of linear equations a1x+b1y+c1=0 and a2x+b2y+c1=0  will have unique solution when a1a2b1b2.
    Here, a1=k,b1=-4,a2=6,b2=-12.
    a1a2=k6,b1b2=-4-12
    For the equations to have unique solutions, we should have,
    k6-4-12
     k2
    Therefore, the value of k is all real numbers except 2.
     
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