Solve
$3 x - 5 y + 1 = 0; x - y + 1 = 0$

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Solution

$3 x - 5 y + 1 = 0$
$x - y + 1 = 0 \Rightarrow y = x + 1$

Substitute $y = x + 1$ in $3 x - 5 y + 1 = 0$ we get
$3 x - 5 (x + 1) + 1 = 0$
$3 x - 5 (x + 1) + 1 = 0$
$\Rightarrow 3 x - 5 x - 5 + 1 = 0$
$\Rightarrow - 2 x - 4 = 0$
$\Rightarrow - 2 x = 4$
$\Rightarrow x = - 2$
$∴ x = - 2$

Substitute $x = - 2$ in $x - y + 1 = 0$ we get
$- 2 - y + 1 = 0$
$\Rightarrow - y - 1 = 0$
$∴ y = - 1$

Hence $x = - 2, y = - 1$

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