Lets number the equations;
x + y = 5 -----i
2x - y = -2 -----ii
Let's solve this using the substitution method, lets rewrite equation i as;
x = 5 - y
Substitute this into the equation ii
2(5 - y) - y = -2
10 - 2y - y = -2
Collect like terms
10 + 2 = 3y
12 = 3y , y = 12/3 = 4
Lets substitute y = 4 in equation i, we would have
x + 4 = 5
x = 5-4 = 1
Therefore,
x = 1
y = 4