Solve for x and y:
$4 (x - 2) - 3 (y - 3) = 1$
$6 (x - 2) + 7 (y - 3) = 5$

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Solution

$4 (x - 2) - 3 (y - 3) = 1$
$4 x - 8 - 3 y + 9 = 1$
$4 x - 3 y = 0$
$6 (x - 2) + 7 (y - 3) = 5$
$6 x - 12 + 7 y - 21 = 5$
$6 x + 7 y = 38$
$4 x - 3 y = 0 \times 3$ $12 x - 9 y = 0$
$6 x + 7 y = 38 \times 2$ $12 x + 14 y = 76$
(-) (-) (-)
$- 23 y = - 76$
$y = \frac{76}{23}$
$4 x - 3 y = 0$
$4 x = 3 (\frac{76}{23})$
$x = \frac{228}{92}$
$x = \frac{57}{23}$

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Solve for x and y:

$\frac{5}{x} - \frac{3}{y} = 1, \frac{3}{2 x} + \frac{2}{3 y} = 5 (x \neq 0, y \neq 0) .$

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