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Rajan@2021
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Find the value of a and b for which the system of linear equations has an infinite number of solutions: 2x-3y=7, (a+b)x-(a+b-3)y=4a+b

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This is the basic and conceptual question from linear equations in two variables in which we have given two equations 2x-3y=7, (a+b)x-(a+b-3)y=4a+b and we have to find the value of a and b for which it has infinite solutions

Kindly solve the above equations

RS Aggarwal, Class 10, chapter 3D, question no 23

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1 Answer

  1. The equations are
    2x−3y−7=0
    (a+b)x−(a+b−3)y−(4a+b)=0
    Here, a1​=2,b1​=−3,c1​=−7
    a2​=a+b,b2​=−(a+b−3),c2​=−(4a+b)
    The system of linear equations has infinite solutions
    ∴​a1​​/a2=b1​​/b2=c1/c2​​
    ⇒2/(a+b)=-3/−(a+b−3)​=-7/−(4a+b)​
    ⇒2/(a+b)=3/(a+b−3)​
    ⇒2a+2b−6=3a+3b
    ⇒b=−a−6
    Again, we have
    ⇒3/(a+b−3)​=7/(4a+b)​
    ⇒12a+3b=7a+7b−21
    ⇒5a−4b=−21
    Putting b=−a−6
    ⇒5a−4(−a−6)=−21⇒9a=−45
    ⇒a=−5
    Putting  a=−5 in b=−a−6
    ⇒b=−(−5)−6⇒b=−1
    ⇒a=−5,b=−1

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