Solve for x and y :

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

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

Simplifying first equation :

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

Simplifying second equation :

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

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

⇒ 33x - 136 = 8 - 3x

⇒ 33x + 3x = 136 + 8

⇒ 36x = 144

⇒ x = $\dfrac{144}{36}$ = 4.

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

⇒ y = 8 - 3(4) = 8 - 12 = -4.

Hence, x = 4 and y = -4.