SOLUTION: Hi. I have an inequalities system: -0.5x1 - 3x2 <= 5 x1 + x2 <= 0.5 x1 >= -4 How inequalities system solutions set should look like? Thanks for answer

Let me re-write the given system in this EQUIVALENT but more understandable form:

-0.5x - 3y <= 5,     (1)
    x +  y <= 0.5,   (2)
    x      >= -4.    (3)


Equation (1)  represents the half-plane  y >=      (4)    above the corresponding straight line;

Equation (2)  represents the half-plane  y <= -0.5 - x       (5)    below the corresponding straight line;

Equation (3)  represents the half-plane  x >= -4             (6)    to the right of the corresponding vertical straight line.


All the lines are shown in the Figure below:






Plots  y =  (red),  y = -0.5 - x (green),  x = -4 (blue)


So the solution set is the INTERSECTION of the listed domains, which is the triangle area constrained by the red, green and blue straight lines.


The lines (the sides of the triangle) are INCLUDED to the solution set borders.