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J & K CET Engineering J and K - CET Engineering Solved Paper-2012

  • question_answer
    The number of integer values of m, for which the x-coordinate of the point of intersection  of the lines \[x+y=3\]and \[y=3mx+1\]is also an integer, is                                 

    A)  \[0\]               

    B)  \[1\]                   

    C)  \[2\]               

    D) \[4\]    

    Correct Answer: C

    Solution :

    Given,  \[x+y=3\] and \[y=3mx+1\] \[\therefore \] \[x+3mx+1=3\] \[\Rightarrow \] \[x(1+3m)=2\] \[\Rightarrow \] \[x=\frac{2}{1+3m}\] Since, x is an integer, therefore \[1+3m=\pm 1,\pm 2\] \[\therefore \] \[3m=\pm 1-1,\,\,3m=\pm 2-1\] \[\Rightarrow \] \[m=0,\,-\frac{2}{3},\,\,m=\frac{1}{3},-1\] Since, m is an integer. So, \[m=0\] and \[-1\] exist.


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