We have,

217x + 131y = 913 …(i)

131x + 217y = 827 …(ii)

To solve these equations, we need to simplify them.

So, by adding equations (i) and (ii), we get

(217x + 131y) + (131x + 217y) = 913 + 827

⇒ (217x + 131x) + (131y + 217y) = 1740

⇒ 348x + 348y = 1740

Now dividing it by 348, we get

x + y = 5 …(iii)

Similarly, subtracting equations (i) and (ii),

(217x + 131y) – (131x + 217y) = 913 – 827

⇒ (217x – 131x) + (131y – 217y) = 86

⇒ 86x – 86y = 86

Dividing the equation by 86, we get

x – y = 1 …(iv)

To solve equations (iii) and (iv), we need to make one of the variables (in both the equations) have same coefficient.

Here the variables x & y in both the equations have same coefficients.

⇒ 2x = 6

⇒ x = 3

Substitute x = 3 in eq.(iii)/eq.(iv), as per convenience of solving.

Thus, substituting in eq.(iii), we get

3 + y = 5

⇒ y = 2

Hence, we have x = 3 and y = 2.