Simultaneous Equations Long Questions (Question 1 & 2)


Question 1:
Solve the following simultaneous equations.
y+2x=2 2 x + 1 y =5  Solution:
y+2x=2(1) 2 x + 1 y =5(2) y=22x(3) substitute (3) into (2), 2 x + 1 22x =5 2( 22x )+x x( 22x ) =5 44x=5x( 22x ) 44x=10x10 x 2 10 x 2 14x+4=0 5 x 2 7x+2=0 ( 5x2 )( x1 )=0 5x2=0     or     x1=0 x= 2 5            or     x=1 Substitute values of x into (3), When x= 2 5  ,  y=22( 2 5 )=1 1 5 When x=1 y=22(1)=0 The solutions are x= 2 5 , y=1 1 5  and x=1, y=0 


Question 2:
Solve the following simultaneous equations.
x – 3y + 5 = 3y + 5y2 – 6 – x = 0

Solution:
x – 3y + 5 = 0
x = 3y – 5 -----(1)
3y + 5y2 – 6 – x = 0 -----(2)

Substitute (1) into (2),
3y + 5y2 – 6 – (3y – 5) = 0
3y + 5y2 – 6 – 3y + 5 = 0
5y2 – 1 = 0
5y2  = 1
y±0.447

Substitute the values of y into (1),
When y = 0.447
x = 3 (0.447) – 5
x = –3.659

When y = – 0.447
x = 3 (–0.447) – 5
x = –6.341

The solutions are x = –3.659, y = 0.447 and x = –6.341, y = – 0.447.