The number of common solutions of $x + 2 y = 8$ and $2 x + y = 8$ is _____

0

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1

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2

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Infinite

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Solution

The correct option is A $1$
Given, $x + 2 y = 8$
$\Rightarrow x = 8 - 2 y$ --- $(1)$
Substituting $x$ in $2 x + y = 8$ , we get
$2 (8 - 2 y) + y = 8$
$\Rightarrow 16 - 4 y + y = 8$
$\Rightarrow 3 y = 8$
$\Rightarrow y = \frac{8}{3}$
Substituting in eqn 1 we get
$\Rightarrow x = 8 - 2 (\frac{8}{3}) = \frac{8}{3}$
So, they have one solution.

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