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

  • question_answer Solve for x and y in the following question. \[\frac{2}{x+2y}+\frac{1}{2x-y}+\frac{5}{9}=0,\] \[\frac{9}{x+2y}+\frac{6}{2x-y}+4=0\]

    A)  \[x=1,\text{ }y=2\]               

    B)  \[x=2,\text{ }y=1\]   

    C)  \[x=2,y=\frac{1}{2}\]   

    D)         \[x=\frac{1}{2},y=2\]

    Correct Answer: D

    Solution :

    We have, \[\frac{2}{x+2y}+\frac{1}{2x-y}+\frac{5}{9}=0\] and \[\frac{9}{x+2y}+\frac{6}{2x-y}+4=0\] Let \[\frac{1}{x+2y}=a\]  and \[\frac{1}{2x-y}=b\] Thus equations would reduce to \[2a+b=-\frac{5}{9}\]           .....(1) and \[9a+6b=-\text{ }4\]              .....(2) Solving (1) and (2), we get \[a=\frac{2}{9}\] and \[b=-1\] \[\frac{2}{9}=\frac{1}{x+2y}\] and  \[-1=\frac{1}{2x-y}\] \[\Rightarrow \]  \[2x+4y=9\]                ?..(3) and \[2x-y=-1\]                      ?..(4) Solving (3) and (4), we get \[y=2\]and \[x=\frac{1}{2}\].

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