Solve the following equations by elimination method:

37x + 43y = 123

43x + 37y = 117

Given pair of linear equations is

37x + 43y = 123 …(i)

And 43x + 37y = 117 …(ii)

On multiplying Eq. (i) by 43 and Eq. (ii) by 37 to make the coefficients of x equal, we get the equation as

1591x + 1849y = 5289 …(iii)

1591x + 1369y = 4329 …(iv)

On subtracting Eq. (iii) from Eq. (iv), we get

⇒ 1591x + 1369y – 1591x – 1849y = 4329 – 5289

⇒ – 480y = – 960

⇒ y = 2

On putting y = 2 in Eq. (ii), we get

⇒ 43x + 37(2) = 117 ⇒ 43x + 74 = 117

⇒ 43x = 117 – 74

⇒ 43x = 43

⇒ x = 1

Hence, x = 1 and y = 2 , which is the required solution.