Question 344460
First plot the constraints.
{{{ x+y = 6 }}}
{{{highlight(y1=-x+6)}}}
Plot the line.
{{{graph(300,300,-2,8,-2,8,-x+6)}}}
Next,
{{{ 3x+2y = 13 }}}
{{{2y=-3x+13}}}
{{{highlight(y2=-(3/2)x+13/2)}}}
{{{graph(300,300,-2,8,-2,8,-x+6,-(3/2)x+13/2)}}}
Next,
{{{ 2x+y = 8 }}}
{{{highlight(y3=-2x+8)}}}
{{{graph(300,300,-2,8,-2,8,-x+6,-(3/2)x+13/2,-2x+8)}}}
Find the intersection of {{{y1}}} and {{{y2}}}.
{{{y1=-x+6}}}
{{{y2=-(3/2)x+13/2}}}
{{{-x+6=-(3/2)x+13/2}}}
{{{-2x+12=-3x+13}}}
{{{x=1}}}
Then 
{{{y=-1+6}}}
{{{y=5}}}
(1,5)
.
.
.
Find the intersection of {{{y2}}} and {{{y3}}}.
{{{y2=-(3/2)x+13/2}}}
{{{y3=-2x+8}}}
{{{-(3/2)x+13/2=-2x+8}}}
{{{-3x+13=-4x+16}}}
{{{x=3}}}
Then 
{{{y=-2(3)+8}}}
{{{y=2}}}
(3,2)
.
.
.
Find the y-intercept of {{{y1}}} and the x-intercept of {{{y3}}}.
{{{y1=-x+6}}}
{{{y1=6}}}
(0,6)
.
.
{{{y3=-2x+8}}}
{{{0=-2x+8}}}
{{{2x=8}}}
{{{x=4}}}
(4,0)
.
.
.
Plot the intersection points and the intercepts.
 {{{drawing(300,300,-2,8,-2,8,grid(1),circle(4,0,0.2),circle(0,0,0.2),
circle(0,6,0.2),circle(1,5,0.2),circle(3,2,0.2),graph(300,300,-2,8,-2,8,-x+6,-(3/2)x+13/2,-2x+8))}}}