Question 1010660
{{{2x-y<=4}}} includes the line with equation {{{2x-y=4}}} and half of the x-y plane to one side of that line.
To graph that lien we only need to points.
{{{system(x=0,2x-y=4)}}}-->{{{system(x=0,-y=4)}}}-->{{{system(x=0,y=-4)}}} ,
so point (0,-4) belongs to the line with equation {{{2x-y=4}}} .
{{{system(y=0,2x-y=4)}}}-->{{{system(y=0,2x=4)}}}-->{{{system(y=0,x=2)}}} ,
so point (2,0) belongs to the line with equation {{{2x-y=4}}} .
With those two points we can graph line {{{2x-y=4}}} as
{{{graph(300,300,-5,5,-5,5,2x-4)}}} .
Since point (0,0) , the origin, satisfies {{{2x-y<=4}}} ,
because {{{2*0-0=0<4}}} ,
the half of the x-y plane that is the graph of {{{2x-y<=4}}} is
{{{graph(300,300,-5,5,-5,5,2x-y<=4)}}} , the half of the x-y plane that contains the origin.
We can do the same for {{{x+2y>=6}}} :
{{{system(x=0,x+2y=6)}}}-->{{{system(x=0,2y=6)}}}-->{{{system(x=0,y=3)}}} ,
so point (0,3) belongs to the line with equation {{{x+2y=6}}} .
{{{system(y=0,x+2y=6)}}}-->{{{system(y=0,x=6)}}}- ,
so point (6,0) belongs to the line with equation {{{x+2y=6}}} .
With those two points we can graph line {{{x+2y=6}}} as
{{{graph(300,300,-2,8,-5,5,-0.5x+3)}}} .
Since point (0,0) , the origin, does not satisfy {{{x+2y>=6}}} ,
because {{{0+2*0=0<6}}} ,
the half of the x-y plane that is the graph of {{{2x-y<=4}}} is
{{{graph(300,300,-2,8,-5,5,x+2y>=6)}}} , the half of the x-y plane that does not contain the origin.
So the solution to {{{system(2x-y<=4,x+2y>=6)}}} is graphed as the shaded area below.
{{{drawing(300,300,-2,8,-2,8,
grid(1),blue(line(-2,4,2.8,1.6)),
blue(line(2.8,1.6,6,8)),
blue(line(-1.8,3.9,-1.8,8)),blue(line(-1.4,3.7,-1.4,8)),
blue(line(-1,3.5,-1,8)),blue(line(-0.6,3.3,-0.6,8)),
blue(line(-0.2,3.1,-0.2,8)),blue(line(0.2,2.9,0.2,8)),
blue(line(0.6,2.7,0.6,8)),blue(line(1,2.5,1,8)),
blue(line(1.4,2.3,1.4,8)),blue(line(1.8,2.1,1.8,8)),
blue(line(2.2,1.9,2.2,8)),blue(line(2.6,1.7,2.6,8)),
blue(line(3,2,3,8)),blue(line(3.4,2.8,3.4,8)),
blue(line(3.8,3.6,3.8,8)),blue(line(4.2,4.4,4.2,8)),
blue(line(4.2,4.4,4.2,8)),blue(line(4.6,5.2,4.6,8)),
blue(line(5,6,5,8)),blue(line(5.4,6.8,5.4,8)),
blue(line(5.8,7.6,5.8,8))
)}}}