Solve the following systems of simultaneous linear equations by the elimination method

$5x - 9 = \dfrac{1}{y}$

$x + \dfrac{1}{y} = 3$

$5x - 9 = \dfrac{1}{y} \text{ or } 5x - \dfrac{1}{y} = 9$ ……..(i)

$x + \dfrac{1}{y} = 3$ …….(ii)

Adding eq. (i) and (ii) we get,

$\Rightarrow 5x - \dfrac{1}{y} + x + \dfrac{1}{y} = 9 + 3 \\[1em] \Rightarrow 6x = 12 \\[1em] \Rightarrow x = 2.$

Substituting value of x in eq. (ii) we get,

$\Rightarrow x + \dfrac{1}{y} = 3 \\[1em] \Rightarrow 2 + \dfrac{1}{y} = 3 \\[1em] \Rightarrow \dfrac{1}{y} = 1 \\[1em] \Rightarrow y = 1.$

Hence, x = 2 and y = 1.