First solve for x in the first equation
x + 7y = 0
x = -7y
since x = -7y we can substitute -7y into the other equation wherever there is an x
2x - 8y = 22
2(-7y) - 8y = 22
-14y - 8y = 22
-22y = 22
y = -1
Now let's substitute -1 back into either of the original equations so we can solve for x
x + 7y = 0
x + 7(-1) = 0
x - 7 = 0
x = 7
So your solution set is
(7, -1)