To find the ordered pair solutions for the system of equations y = -x² + 2 and y = x, we can set the two equations equal to each other:
-x² + 2 = x
Now we can rearrange this equation into standard quadratic form by moving everything to one side:
-x² + x + 2 = 0
We can solve this quadratic equation using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
where a = -1, b = 1, and c = 2
Plugging these values into the formula, we get:
x = (-1 ± √(1 - 4(-1)(2))) / 2(-1)
x = (-1 ± √9) / (-2)
x = (-1 ± 3) / (-2)
So the solutions for x are x = -1 and x = -2.
To find the corresponding values of y, we can plug these values of x into either of the original equations. Let's use y = x:
When x = -1, y = -1
When x = -2, y = -2
Therefore, the ordered pair solutions for this system of equations are (-1, -1) and (-2, -2).