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

  • question_answer The solution of the system of equations \[\frac{2x+5y}{xy}=6\] and \[\frac{4x-5y}{xy}+3=0\] (where \[x\ne 0,\,\,y\ne 0\]), is ____.

    A)  1,2                             

    B)  0, 0                

    C)  \[-1,\text{ }2\]         

    D)         \[1,-2\]

    Correct Answer: A

    Solution :

    We have, \[\frac{2x+5y}{xy}=6\] or \[\frac{2}{y}+\frac{5}{x}=6\]   ?.(1) Also, \[\frac{4x-5y}{xy}=-3\] or \[\frac{4}{y}-\frac{5}{x}=-3\]       ....(2) Let \[\frac{1}{y}=a\]  and \[\frac{1}{x}=b\] So, (1) and (2) become \[2a+5b=6\]                               ...(3) and,  \[4a-5b=-3\]                      ...(4) Adding (3) and (4), we get \[a=\frac{1}{2}\]  and \[b=1\]                   [From (3)] \[\therefore \]   \[x=1\]  and \[y=2\]


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