Solve :

217x + 131y = 913

131x + 217y = 827

On adding both equations, we get:

⇒ 348x + 348y = 1740

⇒ 348(x + y) = 1740

⇒ x + y = $\dfrac{1740}{348}$

⇒ x + y = 5 ………………(1)

On subtracting both equations, we get:

⇒ 86x - 86y = 86

⇒ 86(x - y) = 86

⇒ x - y = $\dfrac{86}{86}$

⇒ x - y = 1 ………………(2)

On adding equations (1) and (2), we get:

$\begin{matrix} & x & + & y & = & 5 \ & x & - & y & = & 1 \ \hline & 2x & & & = & 5 + 1\ \Rightarrow & 2x & & & = & 6 \end{matrix}$

⇒ x = $\dfrac{6}{2}$

⇒ x = 3

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

⇒ 3 + y = 5

⇒ y = 5 - 3

⇒ y = 2

Hence, the value of x = 3 and y = 2.