on comparing the ratios a1/a2, b1/b2 and c1/c2, find out whether the following pair of linear equations are consistent , or inconsistent​

Question

on comparing the ratios a1/a2, b1/b2 and c1/c2, find out whether the following pair of linear equations are consistent , or inconsistent​

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Audrey 4 weeks 2021-10-29T18:30:57+00:00 1 Answer 0 views 0

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    2021-10-29T18:32:34+00:00

    HERE IS YOUR ANSWER MATE…..;

    (i) Given : 3x + 2y = 5 or 3x + 2y – 5 = 0 :-

    and 2x – 3y = 7 or 2x – 3y – 7 = 0

    Comparing the above equations with a1x + b1y + c1=0

    And a2x + b2y + c2 = 0

    We get,

    a1 = 3, b1 = 2, c1 = -5

    a2 = 2, b2 = -3, c2 = -7

    a1/a2 = 3/2, b1/b2 = 2/-3, c1/c2 = -5/-7 = 5/7

    Since, a1/a2≠b1/b2 the lines intersect each other at a point and have only one possible solution.

    Hence, the equations are consistent.

    (ii) Given 2x – 3y = 8 and 4x – 6y = 9 :-

    Therefore,

    a1 = 2, b1 = -3, c1 = -8

    a2 = 4, b2 = -6, c2 = -9

    a1/a2 = 2/4 = 1/2, b1/b2 = -3/-6 = 1/2, c1/c2 = -8/-9 = 8/9

    Since, a1/a2=b1/b2≠c1/c2

    Therefore, the lines are parallel to each other and they have no possible solution. Hence, the equations are inconsistent.

    Hope It’s Helpful….:)

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