To solve this system of equations, you can use the method of elimination or substitution.
Method 1: Elimination
To eliminate the variable y, we can add the two equations together:
(X + y) + (X - y) = 8 + 2
2X = 10
X = 5
Now, substitute the value of X back into one of the original equations to solve for y:
5 + y = 8
y = 8 - 5
y = 3
So the solution to the system of equations is X = 5 and y = 3.
Method 2: Substitution
From the second equation, we can solve for X in terms of y:
X = y + 2
Substitute this expression for X into the first equation:
(y + 2) + y = 8
2y + 2 = 8
2y = 8 - 2
2y = 6
y = 6/2
y = 3
Now substitute the value of y back into the expression for X:
X = 3 + 2
X = 5
Again, the solution to the system of equations is X = 5 and y = 3.
X+y=8
X-y=2
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