The solution region of the inequalities are:
1) (x, y) , (x > 2.8 & y ε -1.5)
2) (x, y) , (x <= - 2.5& y ε R)
3) (x,y) (x ε R & y < -2).
4) (x,y) (x <= -5 R & y ε R
5) (x, y) , (x > 6 & y ε R).
6) No solution
How to determine solutions of inequalities graphically.
The region that contains the solutions of inequalities on a graph is often referred to as the "solution region" or "feasible region." In a two-variable scenario, such as graphing linear inequalities, this region represents all the points (x, y) that satisfy the given set of inequalities.
For systems of inequalities, the solution region is the overlapping or intersection of the individual solution regions for each inequality
Therefore considering the graphs
1) The solution is the point of intersection of the lines. The includes all x- values greater than 2.8 and y = -1.5. (x, y) , (x > 2.8 & y ε -1.5)
2) The solution is all I x-values less equals to -2.5 and and all y-values.(x, y) , (x <= - 2.5& y ε R)
3)The solutions all all real values of x and y less than -2. That's (x,y) (x ε R & y < -2).
4) The solutions are x values less than equals to -5 and all real values of y. That's (x,y) (x <= -5 R & y ε R).
5) The solutions include x values greater than 6 and all real values of y. (x, y) , (x > 6 & y ε R).
6) The two line graphs are parallel because they have same slope. The slope is 2. They do not intersect so, no solution.