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Rajan@2021
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Write the number of solutions of the following pair of linear equations: x+2y-8=0, 2x+4y=16

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An important and conceptual question from linear equations in two variables in which we have to find the number of solutions of given equations x+2y-8=0, 2x+4y=16

Kindly solve the above equations

RS Aggarwal, Class 10, chapter 3F, question no 1

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  1. x+2y=8
    And 2x+4y=16
    These given equations are in the form:
    a1x+b1y+c1=0 and
    a2x+b2y+c2=0
    Where
    a1=1,b1=2 and c1=8
    a2=2,b2=4 and c2=16
    a1/a2=1​/2, b1/b2=2/4=1/2
    As we know, the condition for the equations to have infinitely many solutions is

    a1/a2=b1/b2=c1​/c2
    So, system has infinitely many solutions

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