Question

$$\begin{gathered} 37x+43y=123, \\ 43x+37y=117. \end{gathered}$$

Answer 1

The given equations are:

37x + 43y = 123 ...........(i)
43x + 37y = 117 .............(ii)

On adding (i) and (ii), we get:
80x + 80y = 240
⇒80(x + y) = 240
⇒ (x + y) = 3 .............(iii)

On subtracting (i) from (ii), we get:
6x − 6y = −6
⇒ 6(x − y) = −6
⇒ (x − y) = −1 ............(iv)

On adding (iii) and (iv), we get:
2x = 3 − 1 = 2 ⇒ x = 1

On subtracting (iv) from (iii), we get:
2y = 3 + 1 = 4
⇒ y = 2

Hence, the required solution is x = 1 and y = 2.