Use the graphing method to solve the system of linear equations:

y = -x + 3 and y = x - 1
A (-1,2)(-1,2)
B (0,3)(0,3)
C (1,0)(1,0)
D (1,2)(1,2)
E (2,1)

To solve this system of equations using the graphing method, we need to plot the lines represented by each equation on a graph and find their point of intersection.

First, let's graph the equation y = -x + 3. This is a line that crosses the y-axis at (0, 3) and has a slope of -1.

Next, let's graph the equation y = x - 1. This is a line that crosses the y-axis at (0, -1) and has a slope of 1.

The point of intersection of these two lines is (1, 2).

Therefore, the answer is A: (-1,2)(-1,2)