Find the value of k in the equations: $x + k y = 1$ and $x - y = 2$ have infinitely many solutions.

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Solution

The correct option is B -1
The general form of linear equation written as,
$a_{1} x + b_{1} y + c_{1} = 0$
$a_{2} x + b_{2} y + c_{2} = 0$
Add comparing the coefficients of the variables, we find the value of k
$x + k y = 1$ ---- (1)
$x - y = 2$ ---- (2)
$a_{1} = 1; b_{1} = k; c_{1} = 1$
$a_{2} = 1; b_{2} = - 1; c_{1} = 2$
$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$
$\frac{1}{1} = \frac{k}{- 1}$
$k = - 1$

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