Find the dependent pair of linear equations from the following.

x + 2 y = 4 2 x + 4 y = 8

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x + 3 y = 4 x + 4 y = 15

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3 x + 2 y = 8 2 x + 3 y = 12

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x + 4 y = 10 2 x + 2 y = 6

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Solution

The correct option is A $x + 2 y = 4 2 x + 4 y = 8$
For dependent pair of lines, $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}} .$

From the given options.
For $x + 2 y = 4 & 2 x + 4 y = 8$
$\frac{1}{2} = \frac{2}{4} = \frac{4}{8} = \frac{1}{2} \to$ Its a dependent pair of linear equations

For $x + 3 y = 4 & x + 4 y = 15$
$\frac{1}{1} \neq \frac{3}{4} \neq \frac{4}{15} \to$ Its not a dependent pair of linear equations

For $3 x + 2 y = 8 & 2 x + 3 y = 12$
$\frac{3}{2} \neq \frac{2}{3} = \frac{8}{12} \to$ Its not a dependent pair of linear equations

For $x + 4 y = 10 & 2 x + 2 y = 6$
$\frac{1}{2} \neq \frac{4}{2} = \frac{10}{6} \to$ Its not a dependent pair of linear equations

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