Question

Translate to a system of equations and solve using the addition method.
The sum of two numbers is88. The difference is 22.Find the numbers?

My answer:
I started but i think that i am wrong.

x + y = 88
y = -x +88
y = -1x + 88

now once i substituted
x -1x + 88 = 88

see i don't know if i am doing this correctly.

You wrote only one equation and you need two.
x+y=88 is ok
The second equation is
x-y=22.Also note that the problem asks for a solution by addition, not by substitution.
solve for x and y.

so then that means that the solution is (55,33)

yes