Solve :

$4x + \dfrac{x - y}{8}$ = 17

$2y + x - \dfrac{5y + 2}{3}$ = 2

Given,

1st equation :

$\Rightarrow 4x + \dfrac{x - y}{8} = 17 \\[1em] \Rightarrow \dfrac{32x + x - y}{8} = 17 \\[1em] \Rightarrow 33x - y = 136 \\[1em] \Rightarrow y = 33x - 136 …….(1)$

2nd equation :

$\Rightarrow 2y + x - \dfrac{5y + 2}{3} = 2 \\[1em] \Rightarrow \dfrac{6y + 3x - 5y - 2}{3} = 2 \\[1em] \Rightarrow y + 3x - 2 = 6 \\[1em] \Rightarrow y = 8 - 3x ……..(2)$

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

⇒ 33x - 136 = 8 - 3x

⇒ 33x + 3x = 8 + 136

⇒ 36x = 144

⇒ x = $\dfrac{144}{36}$ = 4.

Substituting value of x in equation (1), we get :

⇒ y = 33(4) - 136 = 132 - 136 = -4.

Hence, x = 4 and y = -4.