Solve the pair of linear equation …

The given equations are
37x + 43y = 123 ... (i)
43x + 37y = 117. ... (ii)
Clearly, the coefficients of x and y in one equation are interchanged in the other.
Adding (i) and (ii), we get
(37x + 43y) + (43x + 37y)  = 123 + 117
(37 + 43)x+ (43 + 37)y = (123 +117)
{tex} \Rightarrow{/tex}80x + 80y = 240
{tex} \Rightarrow{/tex}80(x + y) = 240
{tex} \Rightarrow{/tex} x + y = 3 ....... (iii)
Subtracting (i) from (ii), we get
(37x + 43y) -  (43x + 37y)  = 123 - 117
6x - 6y = -6
{tex}\Rightarrow{/tex} 6 (x - y) = -6
{tex}\Rightarrow{/tex} x - y = -1 ... (iv)
Adding (iii) and (iv), we get
(x + y) + (x - y) = 3 + (-1)
{tex}\Rightarrow{/tex} x + y + x - y = 2
{tex}\Rightarrow{/tex} 2x = 2
{tex}\Rightarrow{/tex} x = 1.
Subtracting (iv) from (iii), we get
(x + y) - (x - y) = 3 - (-1)
{tex}\Rightarrow{/tex}x + y - x + y = 4
{tex}\Rightarrow{/tex}2y = 4
{tex}\Rightarrow{/tex} y = 2.
Hence, x = 1 and y = 2.