Solve the following simultaneous equations:

$5x - 9 = \dfrac{1}{y}, x + \dfrac{1}{y} = 3$

Equations:

$\Rightarrow 5x - 9 = \dfrac{1}{y} \text{ ….(1)} \\[1em] \Rightarrow x + \dfrac{1}{y} = 3 \\[1em] \Rightarrow \dfrac{1}{y} = 3 - x \text{ ….(2)}$

From equation (1) and (2), we get :

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

Substituting value of x in equation (2), we get :

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

Hence, x = 2, y = 1.