If $x = 2 k + 1$ and $y = k$ is a solution of the equation $5 x + 3 y - 7 = 0$ , find the value of $k$ .

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Solution

Given $x = 2 k + 1$ and $y = k$ is the solution of equation 5x+3y-7=0
$5 x + 3 y - 7 = 0$
Put the value of $x = 2 k + 1$ and $y = k$ we get
$5 (2 k + 1) + 3 (k) - 7 = 0$
$\Rightarrow 10 k + 5 + 3 k - 7 = 0$
$\Rightarrow 13 k - 2 = 0$
$\Rightarrow 13 k = 2$
$\Rightarrow k = \frac{2}{13}$

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