10th Class Mathematics Pair of Linear Equations in Two Variables Question Bank Pair of Linear Equations in Two Variables

  • question_answer How many values of c, for which the system of equations \[6x+3y=c-3,\text{ }12x+cy=c\] has infinitely many solutions?

    A)  1                                

    B)  2                    

    C)         3                    

    D)         Infinite

    Correct Answer: A

    Solution :

    Given equations are \[6x+3y=c-3\] and \[12x+cy=c\] For infinitely many solutions, \[\frac{6}{12}=\frac{3}{c}=\frac{c-3}{c}\] Taking first two members, we have             \[\frac{1}{2}=\frac{3}{c}\,\,\Rightarrow \,\,c=6\] Thus, only one value of c exists.

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