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

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

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

Solving 1st equation,

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

Solving 2nd equation,

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

Adding equation (i) and (ii) we get,

⇒ 33x - y + y + 3x = 136 + 8

⇒ 36x = 144

⇒ x = 4.

Substituting value of x in equation (ii) we get,

⇒ y + 3(4) = 8

⇒ y + 12 = 8

⇒ y = -4.

Hence, x = 4 and y = -4.