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Consistency and Inconsistency of Linear Equations in Two Variables

If the pair o...

Question

If the pair of linear equations
$3 x + 2 y = 1$
$(2 k + 1) x + (k + 2) y = k - 1$
Has infinitely many solution, then the value of k is

A

2

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B

4

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C

3

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D

5

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Solution

The correct option is A 2
For infinitely many solutions,
$\frac{3}{2 k + 1} = \frac{2}{k + 2} = \frac{1}{k - 1}$

Thus,
$2 (k - 1) = k + 2$
$2 k - 2 = k + 2$
$k = 4$

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