Solve the pair of linear equations $x - y = 28$ and $x - 3 y = 0$ and if the solution satisfies, $y = m x + 5$ , then find $m$ .

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Solution

given $x - y = 28, x - 3 y = 0$

$\Rightarrow 28 + y = 3 y$

$\Rightarrow 2 y = 28, y = 14$

therefore $x = 42$

now substituting these values in $y = m x + 5$

we get $14 = 42 m + 5, m = \frac{9}{42}$

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