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J & K CET Engineering J and K - CET Engineering Solved Paper-2008

  • question_answer
    The number of solutions of the system of equations \[x-y+z=2\] \[2x+y-z=5\] \[4x+y+z=10\] is

    A)  \[\infty \]

    B)  \[1\]

    C)  \[2\]

    D)  \[0\]

    Correct Answer: B

    Solution :

    Given system of equations are \[x-y+z=2\] \[2x+y-z=5\] and \[4x+y+z=10\] Now, \[A=\left| \begin{matrix}    1 & -1 & 1  \\    2 & 1 & -1  \\    4 & 1 & 1  \\ \end{matrix} \right|\] \[=1(1+1)+1(2+4)+1(2-4)\] \[=2+6-2\] \[=6\ne 0\] Hence,  it has unique solution.b


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