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Rajan@2021
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Solve for x and y: 6x+5y=7x+3y+1=2(x+6y-1)

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I came across a difficult question from linear equations in two variables in which we have been asked to find the value of variables x and y from the equation 6x+5y=7x+3y+1=2(x+6y-1)

Kindly solve this question

RS Aggarwal, Class 10, chapter 3B, question no 16

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  1. 6x+5y=7x+3y+1=2(x+6y−1)
    6x+5y=7x+3y+1
    ⇒6x+5y−7x−3y=1
    ⇒−x+2y=1
    ⇒2y−x=1
    Again 7x+3y+1=2(x+6y−1)
    7x+3y+1=2x+12y−2
    ⇒7x+3y−2x−12y=−2−1
    ⇒5x−9y=−3
    New set of equations is:
    2y−x=1...(1)
    5x−9y=−3...(2)
    Using substitute method:
    From (1),x=2y−1
    Substitute the value of x in (2).
    5(2y−1)−9y=−3
    ⇒10y−5−9y=−3
    ⇒y=−3+5
    ⇒y=2
    And x=2y−1=2(2)−1=3
    Answer: x=3,y=2

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