Find the consistent pair of linear equations from the following.

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

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2 x + y = - 4 3 x - 2 y = 8

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2 x + 3 y = 4 2 x + 3 y = 8

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4 x + 6 y = 4 2 x + 3 y = 8

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Solution

The correct option is B $2 x + y = - 4 3 x - 2 y = 8$
For consistent pair of lines, $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}} .$

From the given options.
For $x + 2 y = 4 & 2 x + 4 y = 8$
$\frac{1}{2} = \frac{2}{4} = \frac{1}{2} \to$ Its not a consistent pair of linear equations.

For $2 x + y = - 4 & 3 x - 2 y = 8$
$\frac{2}{3} \neq \frac{1}{- 2} \to$ Its a consistent pair of linear equations.

For $2 x + 3 y = 4 & 2 x + 3 y = 8$
$\frac{2}{2} = \frac{3}{3} = 1 \to$ Its not a consistent pair of linear equations.

For $4 x + 6 y = 4 2 x + 3 y = 8$
$\frac{4}{2} = \frac{6}{3} = 2 \to$ Its not a consistent pair of linear equations.

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