Given pair of linear equations is
99x + 101y = 499 …(i)
And 101x + 99y = 501 …(ii)
On multiplying Eq. (i) by 101 and Eq. (ii) by 99 to make the coefficients of x equal, we get the equation as
9999x + 10201y = 50399 …(iii)
9999x + 9801y = 49599 …(iv)
On subtracting Eq. (iii) from Eq. (iv), we get
⇒ 9999x + 9801y – 9999x – 10201y = 49599 – 50399
⇒ 9801y – 10201y = 49599 – 50399
⇒ – 400y = – 800
⇒ y = 800/400
⇒ y = 2
On putting y = 2 in Eq. (i), we get
⇒ 99x + 101(2) = 499
⇒ 99x + 202 = 499
⇒ 99x = 297
⇒ x = 297/99
⇒ x = 3
Hence, x = 3 and y = 2 , which is the required solution.
