Question 871241
You can treat the two inequalities as equations and find that point of intersection.  


{{{8y=-9x+72}}}
{{{y=(-9x+72)/8}}}


{{{-4y=7x+28}}}
{{{y=(7x+28)/(-4)}}}


{{{(-9x+72)/8=(7x+28)/(-4)}}}
{{{(72-9x)/8=(7x+28)/(-4)}}}
mult b.s. by 8
{{{72-9x=-2(7x+28)}}}
{{{72-9x=14x-56}}}
{{{72+56=14x+9x}}}
23x=
{{{highlight(x=128/23)}}}, meaning {{{highlight(y=63/23)}}}


Does that point satisfy the inequality system?
9x+8y<72  AND  -7x-4y<=28
9(128/23)+8(63/23)<72  AND -7(128/23)-4(63/23)<=28 ?
IF BOTH TRUE, then you include this intersection point; otherwise exclude this point.