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

2x = 4

⇒ x = 2

On subtracting (iv) from (iii), we get:

2y = 5 + 1

2y = 6

⇒ y = 3

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