Solve, using cross-multiplication

$5 x + 4 y + 14 = 0$
$3 x = - 10 - 4 y$

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Solution

$\frac{x}{b_{1} c_{2} - b_{2} c_{1}} = \frac{y}{c_{1} a_{2} - c_{2} a_{1}} = \frac{1}{a_{1} b_{2} - a_{2} b_{1}}$ --A. That means, $x = \frac{(b_{1} c_{2} - b_{2} c_{1})}{(a_{1} b_{2} - a_{2} b_{1})}$

$y = (c_{1} a_{2} - c_{2} a_{1}) (a_{1} b_{2} - a_{2} b_{1})$

$a_{1} = 5$
$b_{1} = 4$
$c_{1} = 14$

$a_{2} = 3$
$b_{2} = 4$
$c_{2} = 10$

$x = (b_{1} c_{2} - b_{1} c_{1}) / (a_{1} b_{2} - a_{2} b ₁)$

$y = (c_{1} a_{2} - c_{2} a_{1}) / (a_{1} b_{2} - a_{2} b_{1})$

$x = 40 - \frac{56}{20} - 12$

$y = 42 - \frac{50}{20} - 12$

$∴ x = - 2$
$∴ y = - 1$

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3x – 4y = 10 and 8x + 5y = 11

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