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Find the Value (S) of K for Which the Pair of Equations { K X + 2 Y = 3 3 X + 6 Y = 10 Has a Unique Solution. - Mathematics

Sum

Find the value (s) of k for which the pair of equations

`{(kx,+,2y,=,3),(3x,-,6y,=,10):}" has a unique solution"`
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Solution

The given equation is:

kx + 2y = 3
3x + 6y = 10

For a unique solution,

`a_1/a_2 ≠ b_1/b_2`

where `a_1 = k, a_2 = 3, b_1= 2, b_2 = 6`

`k/3 ≠ 2/6`

⇒ k ≠ 1

For all values of k except 1, the given linear equations will have unique solution.

Concept: Linear Equations in Two Variables
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