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

  • question_answer If the system of equations \[2x+3y=7\]             \[2ax+(a+b)y=28\] has infinitely many solutions, then the values of a and b respectively are ____.

    A)  2. 5                

    B)  5, 8                

    C)  4, 8            

    D)         3, 6    

    Correct Answer: C

    Solution :

    Given equations are                       \[2x+3y=7\]and \[2ax+(a+b)\,y=28\] For infinitely many solutions, we have                      \[\frac{2}{2a}=\frac{3}{a+b}=\frac{7}{28}\] Taking first two members, we get \[2a+2b=6a;\] \[\Rightarrow \]  \[4a=2b\]      \[\Rightarrow \] \[2a=b\]       .....(1) Also,    \[\frac{2}{2a}=\frac{7}{28}\]  \[\Rightarrow \] \[a=4\] From (1) and (2), we have \[2(4)=b\,\,\Rightarrow \,\,\,b=8\]

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