X+y=3
y+x= 5

help please

Solve by elimination ie eliminate x or y from the equations by performing operations on them.
first label the equations , to follow the process.
x - y = 5 (1)
x+ y = 3 (2)
If (1) and (2) are added then y will be eliminated.
(1) + (2) gives : 2x = 8 → x = 4
now substitute this value of x into either of the 2 equations and solve for y.
let x = 4 in (1) : 4 - y = 5 → -y = 1 → y = -1
check in (1) : 4-(-1) = 4+1 = 5
check in(2) : 4 - 1 = 3

So your answer is x = 4 , y = -1