Question

Find all solutions of the system of equations.

x−16y^2 =0
4y-x^2= 0

Answer 1

one solution will be 0,0

Answer 2

substitute the value of x from first equation on the second equation
x−16y^2 =0 => x = 16y^2
4y-x^2= 0

4y-(16y^2)^2= 0
4y(1 - 64y^3) = 0
y^3 = 1/64
y = 1/4

putting this value on first equation,
x = 16*(1/4)^2 = 1

so your two real solutions are 0,0 and 1,1/4

theoretically it should have 4 solutions, so other solution are imaginary.

Answer 3

complete solution is here
http://www.wolframalpha.com/input/?i=x%E2%88%9216y%5E2+%3D0%2C+4y-x%5E2%3D+0

Answer 4

Awesome. Thank you!

Answer 5

You are welcome!!!