In the following question, two equations numbered I and II are given. Solve both the equations and mark the appropriate option:
I. $2 x + 3 y = 14$
II. $4 x + 2 y = 16$

if x

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if x > y

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if x

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if x < y

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if x = y, or no definite relationship can be established between x and y

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Solution

The correct option is D if x < y
$2 x + 3 y = 14 4 x + 2 y = 16$

On solving, (i) $\times$ 2 - (ii) we get,
$4 x + 6 y - 4 x - 2 y = 28 - 16$
$\Rightarrow 4 y = 12 \Rightarrow y = 3$

So, the value of x will be -
$2 x + 3 \times 3 = 14$
$\Rightarrow 2 x = 14 - 9 = 5 \Rightarrow x = \frac{5}{2}$

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