Simultaneous Equations, Long Questions


Simultaneous Equations, Long Questions 
Question 7:
Solve the following simultaneous equations.
5y – 6x = 2
4y x 3x y =4.

Solution:
5y – 6x = 2 ----- (1)
4y x 3x y =4 ------- (2) From (1), y= 2+6x 5             

Substitute (3) into (2),
4( 2+6x 5 ) x 3x ( 2+6x 5 ) =4 8+24x 5x 15x 2+6x =4 ( 8+24x )( 2+6x )( 15x )( 5x ) 5x( 2+6x ) =4

16 + 48x + 48x + 144x2 – 75x2 = 20x (2 + 6x)
69x2 + 96x + 16 = 40x + 120x2
51x2 – 56x – 16 = 0
(3x – 4)(17x + 4) = 0
3x – 4 = 0        or         17x + 4 = 0
x= 4 3           or          x= 4 17   

Substitute x= 4 3  into (3), y= 2+6( 4 3 ) 5 =2

Substitute x= 4 17  into (3), y= 2+6( 4 17 ) 5 = 2 17

The solutions are ( 4 3 ,2 ) and ( 4 17 , 2 17 ).