we have that
[tex]x-y=2[/tex]
solve for y
[tex]y=x-2[/tex] -------> equation [tex]1[/tex]
so
Assume a value of x and then with the equation calculate the value of y
case N 1) Assume [tex]x=-5[/tex]
substitute in the equation [tex]1[/tex] and find the value of y
[tex]y=-5-2=-7[/tex]
therefore
the answer Part 1) is
The pair of negative integers is [tex](-5,-7)[/tex]
case N 2) Assume [tex]x=-10[/tex]
substitute in the equation [tex]1[/tex] and find the value of y
[tex]y=-10-2=-12[/tex]
therefore
the answer Part 2) is
The pair of negative integers is [tex](-10,-12)[/tex]