We have,

71x + 37y = 253 …(i)

37x + 71y = 287 …(ii)

To solve these equations, we need to simplify them.

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

(71x + 37y) + (37x + 71y) = 253 + 287

⇒ (71x + 37x) + (37y + 71y) = 540

⇒ 108x + 108y = 540

Now dividing it by 108, we get

x + y = 5 …(iii)

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

(71x + 37y) – (37x + 71y) = 253 – 287

⇒ (71x – 37x) + (37y – 71y) = - 34

⇒ 34x – 34y = - 34

Dividing the equation by 34, 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 = 4

⇒ x = 2

Substitute x = 2 in eq.(iii)/eq.(iv), as per convenience of solving.

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

2 + y = 5

⇒ y = 3

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