the system of inequalities is
![y> (1/3)x](/tex.php?f=y> (1/3)x)
![y\leq-x+4](/tex.php?f=y\leq-x+4)
step-by-step explanation:
step 1
find the equation of the dashed line
we have the points
(0,0) and (3,1)
the line passes through the origin, so, is a direct variation
find the slope
![m=y/x=1/3](/tex.php?f=m=y/x=1/3)
the equation of the dashed line is
![y=(1/3)x](/tex.php?f=y=(1/3)x)
the solution of the inequality a s the shaded area above the dashed line
therefore
the equation of the inequality a is
![y> (1/3)x](/tex.php?f=y> (1/3)x)
step 2
find the equation of the solid line
we have the points
(4,0) and (0,4)
find the slope
![m=(4-0)/(0-4)=-1](/tex.php?f=m=(4-0)/(0-4)=-1)
the equation of the solid line is
![y=-x+4](/tex.php?f=y=-x+4)
the solution of the inequality b s the shaded area below the solid line
therefore
the equation of the inequality b is
![y\leq-x+4](/tex.php?f=y\leq-x+4)
step 3
the system of inequalities is
![y> (1/3)x](/tex.php?f=y> (1/3)x)
![y\leq-x+4](/tex.php?f=y\leq-x+4)