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Rajan@2021
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Show graphically that the following given systems of equations has indefinitely many solutions: x-2y=5, 3x-6y=15

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This is the basic and conceptual question from linear equations in two variables in which we have given the two equations x-2y=5, 3x-6y=15 and we have to show graphically that the following given systems of equations has indefinitely many solutions

Kindly solve the above equation

RS Aggarwal, Class 10, chapter 3A, question no 25

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  1. x2y=5….(1)
    3x6y=12……(2)
    Isolate x from equation (1) and find the value of x and y.
    x2y=5
    or x=5+2y

    x y
    5 0
    3  1
    1 2

    Similarly, isolate x from equation (2) and find the values of x and y.
    3x6y=15
    or x=(15+6y)/3

    x y
    7 1
    1 3
    3 4

    Graph:
    All the points lie on the same line.
    Which shows that, lines coincide each other. Hence, the system has infinite many solutions.

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