Solve : $10 x + 3 y = 75$ ; $6 x - 5 y = 11$

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Solution

$10 x + 3 y = 75$

$6 x - 5 y = 11 \Rightarrow 6 x = 5 y + 11$

$x = \frac{5 y + 11}{6}$

$10 \frac{(5 y + 11)}{6} + 3 y = 75$

$\Rightarrow \frac{25 y + 55}{3} + 3 y = 75$

$\Rightarrow 24 y + 55 + 9 y = 225$

$34 y = 170 \Rightarrow y = 5$

$x = \frac{5 \times 5 + 11}{6} = \frac{36}{6} = 6$

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