CBSE Class 10 Answered
Dear Student,
(a+2b)x + (2a-b)y = 3...............(1)
&
2 (a-2b)x + (2a+b)y = 3............(2)
Multiplying eqn (1) by 2.(a-2b); and eqn (2) by (a+2b), we get
2.(a-2b).(a+2b)x +2.(a-2b).(2a-b)y = 3.2.(a-2b)...................(3)
& 2.(a-2b).(a+2b)x + (2a+b).(a+2b)y = 3.(a+2b)....................(4)
Subtract eqn(4) from eqn(3), and hence eliminating 'x'; we get:
(2a2-15ab+2b2)y = 18b-3a
=> y = 3.(6b-a)/(2a2-15ab+2b2)
Similarly, multiplying eqn(1) by (2a+b) and eqn(2) by (2a-b);
(a+2b).(2a+b)x + (2a-b).(2a+b)y = 3.(2a+b)..................(5)
2 (a-2b).(2a-b)x + (2a+b).(2a-b)y = 3.(2a-b)..................(6)
Subtracting eqn(6) from eqn(5), and hence eliminating 'y, we get:
(-2a2+11ab-2b2)x= 6ab
So, x = 6ab/(-2a2+11ab-2b2)
& y = 3.(6b-a)/(2a2-15ab+2b2)
Regards Topperlearning.