Soalan 9:
Selesaikan persamaan-persamaan serentak:
2(x – y) = x + y – 1 = 2x2 – 11y2
[5 markah]
Penyelesaian:
2(x – y) = x + y – 1
2x – 2y = x + y – 1
x= 3y – 1 —- (1)
x + y – 1 = 2x2 – 11y2
2x2– 11y2 – x – y+ 1 = 0 —- (2)
Gantikan (1) ke dalam (2):
2(3y – 1)2– 11y2 – (3y – 1) – y + 1 = 0
2(9y2– 6y + 1) – 11y2 – 3y + 1 – y+ 1 = 0
18y2– 12y + 2 – 11y2 – 4y + 2 = 0
7y2– 16y + 4 = 0
(7y – 2)(y – 2) = 0
Daripada (1):
apabila y= 2,
x= 3(2) – 1 = 5