Answer:
The system of inequalities is
Step-by-step explanation:
step 1
Find the equation of the dashed line with negative slope
The line passes through the points
(0,-2) and (-2,0)
Find the slope
Find the equation of the line in slope intercept form
we have
substitute
The solution of the inequality is the shaded area below the dashed line
therefore
The equation of the inequality A is
step 2
Find the equation of the dashed line with positive slope
The line passes through the points
(0,0) and (4,1)
Find the slope
Find the equation of the line (direct variation)
we have
substitute
The solution of the inequality is the shaded area above the dashed line
therefore
The equation of the inequality B is
therefore
The system of inequalities is