Simultaneous Equations Long Questions (Question 1 & 2)


Question 1:
Solve the following simultaneous equations.
y + 2 x = 2 2 x + 1 y = 5  Solution:
y + 2 x = 2 ( 1 ) 2 x + 1 y = 5 ( 2 ) y = 2 2 x ( 3 ) substitute (3) into (2), 2 x + 1 2 2 x = 5 2 ( 2 2 x ) + x x ( 2 2 x ) = 5 4 4 x = 5 x ( 2 2 x ) 4 4 x = 10 x 10 x 2 10 x 2 14 x + 4 = 0 5 x 2 7 x + 2 = 0 ( 5 x 2 ) ( x 1 ) = 0 5 x 2 = 0      or      x 1 = 0 x = 2 5            or      x = 1 Substitute values of  x  into (3), When  x = 2 5   ,   y = 2 2 ( 2 5 ) = 1 1 5 When  x = 1 y = 2 2 ( 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.

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