Solve for x and y. 

31x + 29y = 33, 

29x + 31y = 27

The given equations are: 

31x + 29y = 33 … (i) 

29x + 31y = 27 … (ii) 

On adding both sides of equations (i) and (ii), we obtain 

60x + 60y = 60 

$\Rightarrow$y = 1 - x …(iii) 

On substituting the value of y from (iii) in equation (i), we obtain 

31x + 29(1 - x) = 33 

$\Rightarrow$31x + 29 - 29x = 33 

$\Rightarrow$x = 2 

$\Rightarrow$y = 1 - 2 

$\Rightarrow$y = -1 

Hence, x = 2 and y = −1 is the solution of the given system of equations.