Find the value of $k$ for which the following pair of linear equations has a unique solution:
$2 x + 3 y = 7; (k - 1) x + (k + 2) y = 3 k$ .

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Solution

For a unique solution, 2/(k - 1) shouldn't be equal to 3/(k + 2);
2/(k-1) = 3/(k+2)
2k+4 = 3k-3
k=7

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2 x + 3 y = 7, (k - 1) x + (k + 2) y = 3 k

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