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)