Solve the following equations by elimination method:

99x + 101y = 499

101x + 99y = 501

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 = 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.