3.3.5 System of Equations, Long Questions (Question 9)


Question 9:
Solve the simultaneous equations:
2 (xy) = x + y – 1 = 2x2 – 11y2  [5 marks]

Solution:
2 (xy) = x + y – 1
2x – 2y = x + y – 1
= 3y – 1 —- (1)

x + y – 1 = 2x2 – 11y2
2x2– 11y2 x y+ 1 = 0 —- (2)

Substitute (1) into (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
y= 2 7 or y=2

From (1):
when y= 2 7 , x=3( 2 7 )1 x= 6 7 1= 1 7

When y = 2,
= 3(2) – 1 = 5

Hence the solutions are,  x= 1 7 ,y= 2 7  or x=5,y=2


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