Find the value of x and y: 

71x + 37y = 253

37x + 71y = 287 

Given system of equations are: 

71x + 37y = 253 —(i) 

37x + 71y = 287 —(ii) 

Adding (i) and (ii) we get,

108x + 108 y =   540

$\Rightarrow$108(x + y) = 540

$\Rightarrow$x + y = 5  —(iii)

Subtract (ii) from (i), we get: 

34x - 34y = -34 

$\Rightarrow$34(x - y) = -34 

$\Rightarrow$x - y = -1 —(iv) 

Add (iii) and (iv), we get: 

2x = 5 - 1 = 4 

x = 2 

Subtract (iv) from (iii), we get: 

2y = 5 + 1 = 6 

y = 3 

Hence, the required solution is x = 2 and y = 3.