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Find the Value(S) Of K for Which the Pair of Equations Kx + 2y = 3 3x + 6y = 10 Has a Unique Solution.

Question

Find the value(s) of k for which the pair of equations
$\{\begin{cases} k x + 2 y = 3 \\ 3 x + 6 y = 10 \end{cases}$ has a unique solution.

Sum

Solution

The given equations are
$k x + 2 y = 3 3 x + 6 y = 10$
For a unique solution,
`a_1/a_2 ≠ b_1/b_2`
Where a₁= k, a₂= 3, b₁ = 2, b₂ = 6.
`k/3 ≠ 2/6`
⇒ k ≠ 1
For all values of k except 1, the given linear equations will have a unique solution.