Consider the two equations 𝑦=3(𝑥+4)2-3 and (𝑥+2)2+(𝑦-2)2=16

Question

Consider the two equations 𝑦=3(𝑥+4)2-3 and (𝑥+2)2+(𝑦-2)2=16 .

How many solutions are there to this system?

Without solving, give a convincing argument explain why there are that many solutions to the system. 

Answer 1

𝑦=3(𝑥+4)2-3

y = (6x + 24) - 3

y = 6x + 21

(𝑥+2)2+(𝑦-2)2=16

(2x + 4) + (2y - 4) = 16

2x + 2y = 16

x + y = 8

y = 8-x

6x + 21 = 8 - x

7x = -13

x = -13/7

y = 69/7