Simultaneous Equations 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= 2x4 3  -------( 3 ) Substitute (3) into (2), ( 2x4 3 ) 2 +4 x 2 =2 ( 4 x 2 16x+16 9 )+4 x 2 =2 4 x 2 16x+16+36 x 2 =18   ( ×9 ) 40 x 2 16x2=0 20 x 2 8x1=0 ( 10x+1 )( 2x1 )=0 x= 1 10   or  x= 1 2 Substitute the values of x into (3), When x= 1 10 , y= 2( 1 10 )4 3 =1 2 5 When x= 1 2 , y= 2( 1 2 )4 3 = 3 3 =1 The solutions are x= 1 10 , y=1 2 5  and x= 1 2 , 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=2 y= b± b 2 4ac 2a y= ( 6 )± ( 6 ) 2 4( 3 )( 2 ) 2( 3 ) y= 6± 12 6 y=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.