Find the value of K for which equation x – Ky = 2, 3x + 2y = 5 has unique solution.

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UPTET 2018 Paper- 2 Maths & Science (Hindi - English/Sanskrit) Hinglish Solution
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  1. \(K \ne \frac {-2} 3\)
  2. \(K = \frac {2} 3\)
  3. \(K \ne \frac {2} 3\)
  4. \(K = \frac {-2} 3\)

Answer (Detailed Solution Below)

Option 1 : \(K \ne \frac {-2} 3\)
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UPTET Paper 1 - Full Test 1 (Hindi - English/Sanskrit)
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Detailed Solution

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Concept:

Consider expression: a1x + b1y + c = 0 and a2x + b2y + c = 0

Condition for the system has unique solution if a1/a2 ≠ b1/b2

Condition for the system has infinite solution if a1/a2 = b1/b2 = c1/c2

Condition for the system has no solution if a1/a2 = b1/b2 ≠ c1/c2

Calculation:

The equation is x – Ky = 2, 3x + 2y = 5

Here, a1 = 1, b1 = -k, a2 = 3, b2 = 2

1/3 ≠ -k/2

≠ -2/3

∴ The required value of K should not be equal to -2/3

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