4.2.4 Simultaneous Equations, Long Questions
Question 7:
Solve the following simultaneous equations.
5y – 6x= 2
4yx−3xy=4.
Solution:
5y – 6x= 2 ----- (1)
4yx−3xy=4 ------- (2)From (1),y=2+6x5
Substitute (3) into (2),
4(2+6x5)x−3x(2+6x5)=48+24x5x−15x2+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=43 or x=−417
Substitute x=43 into (3),y=2+6(43)5=2
Substitute x=−417 into (3),y=2+6(−417)5=217
Question 8:
Solve the following simultaneous equations.
Give your answer correct to three decimal places.
Solution:
Solve the following simultaneous equations.
Give your answer correct to three decimal places.
Solution: