For what values of k will the following pair of linear equations have infinitely many solutions? kx + 3y – (k – 3) = 0 and 12x + ky – k = 0

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Solution

Q.
For what values of k will the following pair of linear equations have infinitely many solutions kx + 3y – (k – 3) = 0 and 12x + ky – k = 0

Ans.
(6)

Comparing with $a_{1} x + b_{1} y = c_{1} and a_{2} x + b_{2} y = c_{2}$

$a_{1} = k, a_{2} = 12, b_{1} = 3, b_{2} - k, c_{1} = k - 3, c_{2} - k$

For infinite solutions, $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$

$∴$ $\frac{k}{12} = \frac{3}{k} = \frac{k - 3}{k} \Rightarrow \frac{k}{12} = \frac{3}{k} \Rightarrow k^{2} = 36 \Rightarrow k = 6$

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