Solve:
$4 x + 5 y = 7$
$3 x + 4 y = 5$

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Solution

$4 x + 5 y = 7$ ...... $(1)$
$3 x + 4 y = 5$ ...... $(2)$
$4 \times (2) - 3 \times (3)$
$12 x + 16 y - 12 x - 15 y = 20 - 21$
$y = - 1$
Substitute $y = - 1$ in $(1)$ we get
$4 x + 5 \times - 1 = 7$
$\Rightarrow 4 x = 7 + 5 = 12$
or $x = \frac{12}{4} = 3$
$∴ x = 3, y = - 1$

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