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What will (k) be for (2x+3y=9) and (4x+ky=18) to have infinitely many solutions?समीकरण (2x+3y=9) और (4x+ky=18) के अनंत हल होने के लिए (k) क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 66
For two linear equations to have infinitely many solutions, the ratios of corresponding coefficients and constants must be equal: a₁/a₂ = b₁/b₂ = c₁/c₂. Here, 2/4 = 9/18 = 1/2, so 3/k = 1/2, which gives k = 6. Therefore, option C is correct. Exam tip: For infinitely many solutions, always check a₁/a₂ = b₁/b₂ = c₁/c₂.दो रैखिक समीकरणों के अनंत हल होने के लिए
1
/
2
=
3
/
k
=
9
/
18
होना चाहिए। यहाँ
2
/
4
=
9
/
18
=
1
/
2
है, इसलिए
3
/
k
=
1
/
2
से
k=6
प्राप्त होता है। अतः सही विकल्प C है। परीक्षा-युक्ति: अनंत हल के लिए अनुपात
a₁
/
a₂
=
b₁
/
b₂
=
c₁
/
c₂
जाँचें।
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