Question

$$\begin{gathered} 71x+37y=253, \\ 37x+71y=287. \end{gathered}$$

Answer 1

The given equations are:
71x + 37y = 253 ..............(i)
37x + 71y = 287 ............(ii)

On adding (i) and (ii), we get:
108x + 108y = 540
⇒ 108(x + y) = 540
⇒ (x + y) = 5................(iii)

On subtracting (ii) from (i), we get:
34x − 34y = −34
⇒ 34(x − y) = −34
⇒ (x − y) = −1...........(iv)

On adding (iii) and (iv), we get:
2x = 5 − 1= 4
⇒ x = 2

On subtracting (iv) from (iii), we get:
2y = 5 + 1 = 6
⇒ y = 3

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