Long Questions (Question 3 & 4)


Question 3:
Solve the following simultaneous equations.
3y – 2x= – 4
y2 + 4x2 = 2

Solution:
3y – 2x= – 4 -----(1)
y2 + 4x2= 2 -----(2)

From (1),y=2x43 -------(3)Substitute (3) into (2),(2x43)2+4x2=2(4x216x+169)+4x2=24x216x+16+36x2=18   (×9)40x216x2=020x28x1=0(10x+1)(2x1)=0x=110  or  x=12Substitute the values of x into (3),When x=110,y=2(110)43=125When x=12,y=2(12)43=33=1The solutions are x=110, y=125 and x=12, y=1.





Question 4:
Solve the simultaneous equations x – 3y = –1 and y + yx – 2x = 0.
Give your answers correct to three decimal places.

Solution:
x – 3y = –1 -----(1)
y + yx – 2x = 0 -----(2)
From (1),
x = 3y – 1 -----(3)
Substitute (3) into (2),
y + y (3y – 1) – 2(3y – 1)  = 0
y + 3y2y – 6y+ 2 = 0
3y2 – 6y + 2 = 0

a=3, b=6c=2y=b±b24ac2ay=(6)±(6)24(3)(2)2(3)y=6±126y=1.577 or 0.423

Substitute the values of y into (3).
When y = 1.577,
x = 3 (1.577) – 1 = 3.731 (correct to 3 decimal places)

When y = 0.423,
x = 3 (0.423) – 1 = 0.269 (correct to 3 decimal places)

The solutions are x = 3.731, y = 1.577 and x = 0.269, y = 0.423.