Solve: $5 x - 3 y + 3 = 0$
$6 x - 5 y - 2 = 0$

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Solution

Given equations are
$5 x - 3 y + 3 = 0$ ...... $(i)$

$6 x - 5 y - 2 = 0$ ...... $(i i)$

$\Rightarrow 5 x - 3 y = - 3$ ........ $(i i i)$

$\Rightarrow 6 x - 5 y = 2$ ......... $(i v)$

On multiplying eq.(iii) by 6 and eq.(iv) by 5, and subtracting the final result, we get

$6 (5 x - 3 y) - 5 (6 x - 5 y) = - 18 - 10$

$\Rightarrow 30 x - 18 y - 30 x + 25 y = - 28$

$\Rightarrow 7 y = - 28$

$\Rightarrow y = \frac{- 28}{7} = - 4$

$∴ y = - 4$

Substitute $y = - 4$ in eq. $(i v)$ we get

$6 x - 5 \times - 4 = 2$

$\Rightarrow 6 x + 20 = 2$

$\Rightarrow 6 x = 2 - 20 = - 18$

$\Rightarrow 6 x = - 18$

$\Rightarrow x = \frac{- 18}{6} = - 3$

$∴ x = - 3, y = - 4$

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