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

  • question_answer Match the following.
    System of equations Solutions
    (P) \[2x-3y+15=0\] \[3x-5=0\] (i) \[x=3,\text{ }y=5\]
    (Q)  \[2x-y=1\] \[4x+3y=27\] (ii) \[x=1,y=4\]
    (R) \[x+2y-3=0\] \[3x-2y+7=0\] (iii) \[x=\frac{5}{3},y=\frac{55}{9}\]
    (S) \[4x+\frac{y}{3}=\frac{16}{3}\] \[\frac{x}{2}+\frac{2y}{4}=\frac{5}{2}\] (iv) \[x=-1,y=2\]
               

    A) (P) \[\to \] (iii); (Q) \[\to \] (iv); (R) \[\to \] (i);  (S) \[\to \] (ii)                           

    B)  (P) \[\to \] (iii); (Q) \[\to \] (i); (R) \[\to \] (iv); (S) \[\to \] (ii)

    C)  (P) \[\to \] (iii); (Q) \[\to \] (ii); (R) \[\to \] (iv); (S) \[\to \] (i)                            

    D)  (P) \[\to \] (ii); (Q) \[\to \] (i); (R) \[\to \] (iv); (S) \[\to \] (iii)                          

    Correct Answer: B

    Solution :

    (P) We have,   \[2x-3y=-15\]          .....(1) and  \[3x-5=0\]  \[\Rightarrow \]  \[x=\frac{5}{3}\] From (1),  \[2\left( \frac{5}{3} \right)-3y=-15\] \[\Rightarrow \]   \[3y=\frac{10}{3}+15\,\,\Rightarrow y=\frac{55}{9}\] (Q) We have,  \[2x-y=1\]                 ?.(1) and    \[4x+3y=27\]                       ?.(2) Multiplying (1) by 2 and then subtracting from (2), we get, \[y=5\]and \[x=3\] (R) We have,    \[x+2y=3\]                 ?.(1) and    \[3x-2y=-7\]                       ?...(2) Multiplying (1) by 3 and then subtracting from (2), we get\[y=2\]and \[x=-1\] (S) We have,\[4x+\frac{y}{3}=\frac{16}{3}\,\,\Rightarrow \,\,12x+y=16\]                                                   ...(1) and   \[\frac{x}{2}+\frac{y}{2}=\frac{5}{2}\,\,\Rightarrow \,\,x+y=5\]              ...(2) Subtracting (2) from (1), we get x= 1 and y = 4

adversite


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