In this problem we can write one equation for each condition so:
[tex]\begin{gathered} x+y=-17 \\ x-y=1 \end{gathered}[/tex]So we solve the second equation for x so:
[tex]x=1+y[/tex]and replace in the first equation :
[tex]\begin{gathered} 1+y+y=-17 \\ 2y=-18 \\ y=-9 \end{gathered}[/tex]and we replace y in the secon equation:
[tex]\begin{gathered} x=1-9 \\ x=-8 \end{gathered}[/tex]So the two integers are: -8 and -9
