Answer
$(0,0)$
$(1,1)$
Work Step by Step
Given the system of equations:
1. $x - y^2 = 0$
2. $y - x^2 = 0$
It asks to find all solutions.
Substitute $y = x^2$
$x = (x^2)^2 = 0$
$x - x^4 = 0$
$x(1-x^3) = 0$
$x = 0, 1$
Substitute the values into the equation
$y - 0^2 = 0$
$y = 0$
$y - 1^2 = 0$
$y = 1$
All solutions:
$(0,0)$
$(1,1)$
