Question 266770
{{{system(green(x+2y<=8), red(2x+y<=0), x>=0, y>=0)}}}

Solve the first two for y

{{{system(green(y<=(8-x)/2), red(y<=-2x), x>=0, y>=0)}}}

plot the boundary equations, which are the original inequalities
with equal signs in place of inequality signs.

{{{system(green(x+2y=8), red(2x+y=0), x=0, y=0)}}}

The last two are the y and x axes, respectively.
{{{x>=0}}} says we are on to the right of the y-axis,
and {{{y>=0)}}} says we are on or above the x-axis, 

{{{drawing(400,254.54545,-2,9,-2,5, graph(400,254.54545,-2,9,-2,5),
green(line(20,-6,-8,8)), red(line(-10,20,7,-14)) )}}}

Since the inequalities for the green and red lines are both
{{{""<=""}}}, the solution set is on or under both of them,
on or right of the y-axis, and on or above the x-axis.

There is only one point that satisfies all these, and that
is the one point (0,0), the origin.

So the solution set is { (0,0) }

Edwin</pre>