Solve for $x$ and $y : x - 4 y - 14 = 0$ , $5 x - y - 13 = 0$

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Solution

Given: Equation of lines $x - 4 y - 14 = 0$ and $5 x - y - 13 = 0$
or
$x - 4 y = 14$ ..... $(1)$

$5 x - y = 13$ ..... $(2)$

Multiplying eq 1 by 5 then subtracting eq 2 from the resultant multiplication i.e, $5 \times (1) - 1 \times (2)$ we get;

$5 x - 20 y - 5 x + y = 70 - 13$

$\Rightarrow - 19 y = 57$

$\Rightarrow y = \frac{57}{- 19} = - 3$

Putting $y = - 3$ in $(1)$ we get;

$x - 4 \times - 3 = 14$

$\Rightarrow x + 12 = 14$

$\Rightarrow x = 14 - 12 = 2$

$∴ x = 2, y = - 3$

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