Solve the following pair of equations:
$6 x + 5 y = 7 x + 3 y + 1 = 2 x + 12 y - 2$

x = 3, y = 2

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x = 1, y = 0

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x = 5, y = 3

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x = 7, y = 1

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Solution

The correct option is A $x = 3, y = 2$
Given, $6 x + 5 y = 7 x + 3 y + 1 = 2 x + 12 y - 2$
By taking first two we get,
$6 x + 5 y = 7 x + 3 y + 1$
$\Rightarrow x - 2 y = - 1$ ....(i)
By taking last two we get,
$7 x + 3 y + 1 = 2 x + 12 y - 2$
$\Rightarrow 5 x - 9 y = - 3$ .....(ii)
On multiplying equation (i) by $5$ . we get,
$5 x - 10 y = - 5$ ....(iii)
Subtracting (ii) from (iii). we get,
$5 x - 10 y - (5 x - 9 y) = - 5 - (- 3)$
$∴ - y = - 2 \Rightarrow y = 2$
On substituting $y = 2$ in (i). we get,
$x - 2 (2) = - 1$
$∴ x = 3$
$∴ x = 3, y = 2$

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Solve for x and y:

$6 x + 5 y = 7 x + 3 y + 1 = 2 (x + 6 y - 1)$

\frac{5}{x - 1} + \frac{1}{y - 2} = 2

\frac{6}{x - 1} - \frac{3}{y - 2} = 1

x \neq 1, y \neq 2)

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