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दो चर वाले रैखिक समीकरण युग्म

Question
CBSEHHIMAH10009998

a और b के किन मानों के लिए, निम्न रैखिक समीकरणों के युग्म के अपरिमित रूप से अनेक हल होंगे?

2x + 3y = 7

( a - b ) x + ( a + b ) y = 3a + b - 2

Solution

2x + 3y = 7
( a - b ) x + ( a + b ) y = 3a + b - 2
a1 = 2, b1 = 3, c1 = 7
a2 = a - b, b2 = a + b, c2 = 3a + b -2
दिए गए रैखिक समीकरणों के युग्म के अनन्त हल के लिए
straight a subscript 1 over straight a subscript 2 space equals space straight b subscript 1 over straight b subscript 2 space equals space straight c subscript 1 over straight c subscript 2

rightwards double arrow space fraction numerator 2 over denominator straight a space minus space straight b end fraction space equals space fraction numerator 3 over denominator straight a space plus space straight b end fraction space equals space fraction numerator 7 over denominator 3 straight a space plus space straight b space minus space 2 end fraction
पहले दो से
fraction numerator 2 over denominator straight a space minus space straight b end fraction space equals space fraction numerator 3 over denominator straight a space plus space straight b end fraction

rightwards double arrow space 2 space left parenthesis space straight a space plus space straight b space right parenthesis space equals space 3 space left parenthesis space straight a space minus space straight b space right parenthesis

rightwards double arrow space 2 straight a space plus space 2 straight b space equals space 3 straight a space minus space 3 straight b

rightwards double arrow space straight a space minus space 5 straight b space equals space 0

fraction numerator 3 over denominator straight a space plus space straight b end fraction space equals space fraction numerator 7 over denominator 3 straight a space plus space straight b space minus space 2 end fraction

rightwards double arrow space 3 space left parenthesis space 3 straight a space plus space straight b space minus space 2 space right parenthesis space equals space 7 space left parenthesis space straight a space plus space straight b space right parenthesis

rightwards double arrow space 9 straight a space plus space 3 straight b space minus space 6 space equals space 7 straight a space plus space 7 straight b

rightwards double arrow space 2 straight a space minus space 4 straight b space minus space 6 space equals space 0

rightwards double arrow space straight a space minus space 2 straight b space minus space 3 space equals space 0


a - 5b = 0    (i)
a - 2b - 3 = 0    (ii)