Step 1) Solve the first equation for #y#:

#x + y - color(red)(x) = 3 - color(red)(x)#

#x - color(red)(x) + y = 3 - x#

#0 + y = 3 - x#

#y = 3 - x#

Step 2) Substitute #3 - x# for #y# in the second equation and solve for #x#:

#3x + y = 5# becomes:

#3x + 3 - x = 5#

#3x - x + 3 = 5#

#2x + 3 = 5#

#2x + 3 - color(red)(3) = 5 - color(red)(3)#

#2x + 0 = 2#

#2x = 2#

#(2x)/color(red)(2) = 2/color(red)(2)#

#(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) = 1#

#x = 1#

Step 3) Substitute #1# for #x# in the solution to the first equation at the end of Step 1 and calculate #y#:

#y = 3 - x# becomes:

#y = 3 - 1#

#y = 2#

The solution is: #x = 1# and #y = 2# or #(1, 2)#