1. Solve the following pairs of equations by reducing them to a pair of linear equations: (i) 1/2x + 1/3y = 2 1/3x + 1/2y = 13/6

Solution: Let us assume 1/x = m and 1/y = n , then the equation will change as follows. m/2 + n/3 = 2 ⇒ 3m+2n-12 = 0…………………….(1) m/3 + n/2 = 13/6 ⇒ 2m+3n-13 = 0……………………….(2) Now, using cross-multiplication method, we get, m/(-26-(-36) ) = n/(-24-(-39)) = 1/(9-4) m/10 = n/15 = 1/5 m/10 = 1/5 and n/15 = 1/5 So, m = 2 and n = 3 1/x = 2 and 1/y = 3 x = 1/2 and y = 1/3