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दो चर वाले रैखिक समीकरण युग्म

Question
CBSEHHIMAH10009928

अनुपातों straight a subscript 1 over straight a subscript 2 comma space straight b subscript 1 over straight b subscript 2 space और space straight c subscript 1 over straight c subscript 2 की तुलना कर ज्ञात कीजिए कि निम्न रैखिक समीकरणों के युग्म संगत हैं या असंगत :

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

Solution

3x + 2y = 5 ; 2x - 3y = 7
straight a subscript 1 space equals space 3 comma space straight b subscript 1 space equals space 2 comma space straight c subscript 1 space equals space 5

straight a subscript 2 space equals space 2 comma space straight b subscript 2 space equals space minus space 3 comma space straight c subscript 2 space equals space 7

therefore space straight a subscript 1 over straight a subscript 2 space equals space 3 over 2 comma space straight b subscript 1 over straight b subscript 2 space equals space fraction numerator negative space 2 over denominator 3 end fraction comma space straight c subscript 1 over straight c subscript 2 space equals space 5 over 7

straight a subscript 1 over straight a subscript 2 space not equal to space straight b subscript 1 over straight b subscript 2
संगत ( अद्वितीय हल ) है।