This is actually a bit of a trick question since the two equations are equivalent.
If you solve #y+4=-2x# for #y# you'll get #y=-2x-4# which is the same as the first equation mentioned in the question.
In a case like this, where you have more variables than equations (there are 2 variables- #x# and #y#, but only equation of #y=-2x-4#) there will actually be infinitely many solutions. You can keep plugging in infinitely many values for #x# and keep getting outputs for #y#.
Notice that #y=-2x-4# is just the equation of a straight line in the form of #y=mx+b#, where the line is continuous for all real numbers (so for all #x#). That's why this this isn't really a "system". The two equations in the question equal each other, hence there is only one net equation, In that net equation, you can have any value for #x# (or #y#) plugged in and a different solution can be found each time.