Question

Solve for x and y:
71x + 37y = 253, 37x + 71y = 287

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) from (i), 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.