x^2+y^2=4
x+y=2
This is the intersecction of a line and a circle
Using the second equation we can write y = 2 - x
And substituting this into the first equation for y, we have
x^2 + (2 - x)^2 = 4 simplify
x^2 + x^2 - 4x + 4 = 4 subtract 4 from both sides and simplify
2x^2 - 4x = 0 factor
2x(x - 2) = 0 setting each factor to 0, we have that x = 0, and x = 2
And using x + y = 2
When x = 0, y = 2
When x = 2, y =0 so the answers are (0,2) (2,0)
Here's a graph......https://www.desmos.com/calculator/eakj6g1q0t