Notice that the y-variable is isolated in Equation (I). Therefore, the most convenient method to solve the given system of equations is the Substitution Method.
x^2+y^2=4 & (I) y=x-2 & (II)
Let's substitute x-2 for y in Equation (I).
Note that in Equation (I) we have a quadratic equation in terms of only the x-variable. There are many ways to solve the given equation. We will solve it by factoring it.
Consider Equation (II) in the given system.
y=x-2
We can substitute x=0 and x=2 into the above equation to find the values for y. Let's start with x=0.
We found that y=0, when x=2. Therefore, our second solution is (2,0).
Graphing
Notice that Equation (I) represents a circle and Equation (II) represents a line. If you need explanations on graphing circles, please refer to this example. If you need explanations on graphing lines, please refer to this other example. Let's graph them and mark the points (0,- 2) and (2,0)!
Both the circle and the line intersect at the points (0,- 2) and (2,0), which confirms our answer.
