how do u answer this? please step by step

*graph and check to solve the linear system
y=-x+3
y=x+1
Thank you very very much!!! :)

y = -x + 3

y = x + 1

rewrite
y + x = 3
y - x = 1

to eliminate the variable x, add the 2 equations together. Since x + -x = 0, the x variable is eliminated

ADD
y + x = 3
y - x = 1
2y = 4
y = 2

to find x, substitute y = 2 in
y + x = 3
2 + x = 3
x = 1

CHECK
x = 1, y = 2
y - x = 1
2 - 1 = 1
1 = 1