solve for one of them
x+y=6
minus x both sides
y=6-x
sub 6-x for y
x(6-x)=-7
6x-x^2=-7
times -1
x^2-6x=7
minus 7 both sides
x^2-6x-7=0
factor
what 2 numbers multiply to -7 and add to get -6?
-7 and 1
(x-7)(x+1)=0
set each to zero
x-7=0
x=7
x+1=0
x=-1
solve for each
y=6-x
for x=7
y=6-7
y=-1
(7,-1)
for x=-1
y=6-(-1)
y=6+1
y=7
(-1,7)
the the numbers are -1 and 7
x=-1 and y=7 works
y=7 and x=-1 works
