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प्रश्न
If the pair of linear equations: a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 is consistent and dependent, then
पर्याय
`(a_1)/(a_2) ≠ (b_1)/(b_2)`
`(a_1)/(a_2) ≠ (b_1)/(b_2) = (c_1)/(c_2)`
`(a_1)/(a_2) = (b_1)/(b_2) ≠ (c_1)/(c_2)`
`(a_1)/(a_2) = (b_1)/(b_2) = (c_1)/(c_2)`
MCQ
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उत्तर
`bb((a_1)/(a_2) ≠ (b_1)/(b_2) = (c_1)/(c_2))`
Explanation:
The three conditions for linear equations are:
1. Unique Solution: `(a_1)/(a_2) ≠ (b_1)/(b_2)` (Consistent and Independent).
2. No Solution: `(a_1)/(a_2) = (b_1)/(b_2) ≠ (c_1)/(c_2)` (Inconsistent).
3. Infinitely Many Solutions: `(a_1)/(a_2) = (b_1)/(b_2) = (c_1)/(c_2)` (Consistent and Dependent).
The question explicitly asks for the consistent and dependent case.
The condition is `(a_1)/(a_2) ≠ (b_1)/(b_2) = (c_1)/(c_2)`.
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