If $x = 2 m + 1$ , and $y = m - 1$ , is the solution of equation $2 x - 3 y + 5 = 0$ , then find $m$ .

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Solution

Given that,
$x = 2 m + 1$ and $y = m - 1$ is the solution of equation $2 x - 3 y + 5 = 0$

i.e., $2 (2 m + 1) - 3 (m - 1) + 5 = 0$

$⟹ 4 m + 2 - 3 m + 3 + 5 = 0$

$⟹ m + 10 = 0$

$∴ m = - 10$

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