It is not clear from the question what is required to be done with the two linear equations.  We can graph them and determine their point of intersection, as shown below

                                                      A                                                D

                  C                                                                                                                        B

Line AB represents the graph of y= -x+3 and CD represents graph of y=x+1.  For graphing the two lines, we can determine any two points on each. Plot these  two points on the graph paper and join  For y=-x+3 these can  be (0,3) and (3,0)..   Similarly, for y=x+1, two points can be (0,1) and (-1,0).

 

The point of intersection is (1,2).

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