Solve the following equations:
$5 x - y = 3$ ,
$y^{2} - 6 x^{2} = 25$ .

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Solution

$y^{2} - 6 x^{2} = 25........ (i) 5 x - y = 3............. (i i) \Rightarrow y = 5 x - 3$
Substituting $y$ in $(i)$
$25 x^{2} + 9 - 30 x - 6 x^{2} = 25 19 x^{2} - 30 x - 16 = 0 {19 x}^{2} - 38 x + 8 x - 16 = 0 19 x (x - 2) + 8 (x - 2) = 0 (19 x + 8) (x - 2) = 0 x = - \frac{8}{19}, 2 y = 5 x - 3 x = - \frac{8}{19} \Rightarrow y = - \frac{8}{19} \times 5 - 3 = - \frac{97}{19} x = 2 \Rightarrow y = 2 \times 5 - 3 = 7$

So the values of $x$ are $- \frac{8}{19}, 2$ and values of $y$ are $- \frac{97}{19}, 7$

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