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

  • question_answer
    If the system of equations \[4x+py=21\] and \[px-2y=15\] has unique solution, then which of the following could be the value of p?
    (I) 6 (II) 66            
    (III) 125 (IV) 6666

    A)  Both (I) and (II)            

    B)  Both (III) and (IV)

    C)  (I), (II) and (III)             

    D)  All of (I), (II), (III) and (IV)

    Correct Answer: D

    Solution :

    (d): \[\frac{{{a}_{1}}}{{{a}_{2}}}\ne \frac{{{b}_{1}}}{{{b}_{2}}}\ne \frac{{{c}_{1}}}{{{c}_{2}}}\Rightarrow \frac{4}{p}\ne \frac{p}{-2}\ne \frac{21}{15}\Rightarrow {{p}^{2}}\ne -8\](always true). Also, \[p\ne \frac{-42}{15}\] \[\therefore \] All values in question satisfy the above.


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