Answer :

konrad509
[tex]x+y=0 \\ x-y=10 \\\\ x=-y\\ x-y=10\\\\ -y-y=10\\ -2y=10\\ y=-5\\\\ x-5=0\\ x=5\\\\ \boxed{(x,y)=(5,-5)}[/tex]
  x+y=0
- x-y=10
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(0)+2y=-10 [x and -x cancel each other out. y minus -y is the same as y+y]
y=-5 
now substitute -5 in for y in either problem:

x+-5=0
x=5