-7x-4y≤28 is the same as -28≤7x+4y or 7x+4y≥-28. This is represented by the orange-red area to the right of the bold red line. 9x+8y<72 is represented by the blue-grey area to the left of the broken blue line. The x and y intercepts are marked.
The intersection of the inequalities is the darker area enclosed by the lines, which intersect when:
7x+4y=-28, y=-7-7x/4 and 9x+8y=72, y=9-9x/8,
-7-7x/4=9-9x/8,
-5x/8=16, x=-128/5=-25.6, and y=-7+44.8=37.8 (as shown).