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 = 960/480
⇒ 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.
