Y=-X-3
X+Y=4
You'll want to get X or Y by itself, which in this question it already is.
After that, use substitution (Plug -X-3 in place of Y in X+Y=4)
Equation should look like X+(-X-3)=4
Solve that equation
X+(-X-3)=4
X+(-X) cancels eachother out, leaving you with (-3)=4
Add 3 to both sides of (-3)=4, leaving you with 0=7
0 Can't equal 7, so this equation has no solutions