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Assertion 9x 12y-7=0 and 6x 8y-14=0 form a consistent pair of the linear equations Reasons A pair of linear equation px qy r=0 and fx gy h= 0 has no solution of p/q=q/g?
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Assertion 9x 12y-7=0 and 6x 8y-14=0 form a consistent pair of the line...
Consistency of the pair of linear equations

  • Given equations are 9x+12y-7=0 and 6x+8y-14=0.

  • These equations can be written in the form of ax+by+c=0 where a, b, and c are constants.

  • So, we have 9x+12y-7=0 can be written as 9x/7+12y/7=1 and 6x+8y-14=0 as 3x/7+4y/7=1.

  • On solving these equations, we get x = 14/3 and y = -5/3.

  • Therefore, the given pair of equations is consistent as they have a solution.



Explanation of p/q=q/g having no solution

  • Let's assume that p/q=q/g=k (where k is some constant).

  • So, we have p = kq and q = kg.

  • Substituting the value of q in the first equation, we get p = k(kg).

  • Substituting the value of p in the second equation, we get kq = kg.

  • Canceling out the common factor k, we get q = g.

  • So, we have p/q=q/g=k=k1 (where k1 is some other constant).

  • Therefore, the given pair of equations has no solution of p/q=q/g as it implies q = g, which is not possible for two different variables.

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Assertion 9x 12y-7=0 and 6x 8y-14=0 form a consistent pair of the linear equations Reasons A pair of linear equation px qy r=0 and fx gy h= 0 has no solution of p/q=q/g?
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