Answer
$(-2,0)$ and $(2, 4)$
Work Step by Step
We can solve the system of equation using the graphical method and then confirm with algebraic operations.
(a) Graphical method: read the coordinates of the intersection points of the line and the circle, we get $(-2,0)$ and $(2, 4)$ which are the solutions to the system.
(b) Confirm with algebraic operations:
Step 1. Use substitution: from equation 1, we get $x=y-2$
Step 2. Substitute it in the second equation to get $(y-2)^2+y^2-4y=4$ or $2y^2-8y=0$ which gives $y=0, 4$ Step 3. Back-substitute the above results into equation 1 to get $x=-2$ and $x=2$
Step 4. The solutions to the system are $(-2,0)$ and $(2, 4)$
