If xy=(-7) and x+y=6 what is x and y?

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

The answer would be option 4