Solve for $x$ and $y$ .
$5 x + 6 y = 7 x + 3 y = 3 (x + 6 y - 6)$

x = 1, y = 3

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x = 2, y = 6

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x = 3, y = 2

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None of these

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Solution

The correct option is D $x = 3, y = 2$
Given, $5 x + 6 y = 7 x + 3 y = 3 (x + 6 y - 6)$
By taking first and third we get,
$5 x + 6 y = 3 (x + 6 y - 6)$
$\Rightarrow 5 x + 6 y = 3 x + 18 y - 18$
$\Rightarrow 2 x - 12 y = - 18$ ....(i)
By taking last two we get,
$7 x + 3 y = 3 (x + 6 y - 6)$
$7 x + 3 y = 3 x + 18 y - 18$
$\Rightarrow 4 x - 15 y = - 18$ .....(ii)
On multiplying equation (i) by $2$ . we get,
$4 x - 24 y = - 36$ ....(iii)
Subtracting (ii) from (iii). we get,
$4 x - 24 y - (4 x - 15 y) = - 36 - (- 18)$
$∴ - 9 y = - 18 \Rightarrow y = 2$
On substituting $y = 2$ in (i). we get,
$2 x - 12 (2) = - 18$
$\Rightarrow 2 x = 6$
$∴ x = 3$
$∴ x = 3, y = 2$

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