On comparing the ratios $straight a subscript 1 over straight a subscript 2 comma straight b subscript 1 over straight b subscript 2 space and space straight c subscript 1 over straight c subscript 2$ find out whether the following pair of linear equations are consistent, or inconsistent.

3x + 2y = 5; 2x - 3y = 7

Solution

3x + 2y = 5 ; 2x - 3y = 7
$Here comma space space space space straight a subscript 1 equals 3 comma space straight b subscript 1 equals 2 comma space straight c subscript 1 equals 5 space space space space space space space space space space space space straight a subscript 2 equals 2 comma space straight b subscript 2 equals negative 3 comma space straight c subscript 2 equals 7 therefore space straight a subscript 1 over straight a subscript 2 equals 3 over 2 comma space straight b subscript 1 over straight b subscript 2 equals fraction numerator negative 2 over denominator 3 end fraction comma space straight c subscript 1 over straight c subscript 2 equals 5 over 7 Clearly comma space straight a subscript 1 over straight a subscript 2 not equal to straight b subscript 1 over straight b subscript 2$
Hence, the given lines are intersecting. So, the given pair of linear equations has exactly one solution and therefore it is consistent.

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Pair Of Linear Equations In Two Variables

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