How many pairs of $x$ and $y$ satisfy the equation $2 x + 4 y = 8$ and $6 x + 12 y - 24 = 0$

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 C Infinite
Given equation-
$2 x + 4 y = 8 (Given equation)$
Dividing the above equation by 2, we have

$x + 2 y = 4 . . . . . . . . . . . . . . . (1)$

Again,
$6 x + 12 y - 24 = 0 (Given equation)$
$\Rightarrow 6 x + 12 y = 24$

Dividing the above equation by 6, we have
$x + 2 y = 4 . . . . . . . . . . . . . . . (2)$

Since both equations are the same, therefore, there will be infinitely many solutions and hence will be infinite pairs of $x$ and $y$ which satisfy the given equations.

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