Could you please go through an example question where you have to solve quadratic simultaneous equations?

Of course - let's solve this question:

Question: Solve the following quadratic simultaneous equations

(1) 2x + y = 4 - x

(2) y² + 4x = 12

Answer:

a) Let us start by re-arranging the first equation:

          2x + y = 4 - x  -> Initial equation

          y = 4 - 3x -> bring the '2x' on the left hand-side to the right hand-side - let's call this equation (3)

b) Substitute (3) into (1):

          (4 - 3x)² + 4x = 12

c) Expand the brackets:

          16 - 24x + 9x² + 4x = 12

d) Re-arrange to get all 'x's onto one side:

          9x² - 20x + 4 = 0

e) Factorise the equation and solve:

          (9x - 2)(x - 2) = 0

          x = 2/9 or 2

f) Substitute the two values of 'x' into equation (3):

          When x = 2/9 -> y = 4 - 3(2/9) = 4 - 6/9 = 10/3

          When x = 2 -> y = 4 - 3(2) = 4 - 6 = -2

g) Therefore the solutions are: (2/9 , 10/3) and (2 , -2)