77 For the system 3Ax By 211 find A and B 3Ax By 11 such

77. For the system {-3Ax + By = 211, find A and B (-3Ax + By =-11, such that x = 3, y = 1 is a solution.

Solution : put x=3 and y=1 in the 2 eqns then the system is

3A +3B =2 -------(1) and - 9A + B = -11 ------(2) multiply eqn 2 by 3

- 27A +3B = - 33 ----(3)

eqn 1 - eqn 3 => 30A = 35 or A = 35/30 = 7/6 Substituting in eqn2 : - 9 ( 7/6) +B =-11

B = - 11 + 63/6 = ( - 66 +63) /6 = - 3/6 = -1/2

ANS : A = 7/6 , B = - 1/2