Answer:
The solution region of a linear inequalities
Explanation:
The solution region of a linear inequalities is the region with coordiates that satisfy the condition of the linear inequalities solution.
For example:
Find the solution region for x + y > 4
Step 1: Draw the line x + y = 4
An easy way to plot the line is to find the points where the line cut across the x and y axis.
1.1 To find a point where the line cut across the x axis i.e the point where y = 0
x + y = 4
x + 0 = 4
Therefore x = 4
The point (x,y) = (4,0) is the point where the line cut across the x axis
1.2 To find a point where the line cut across the y axis i.e the point where x= 0
x + y = 4
0 + y = 4
Therefore y = 4
The point (x,y) = (0,4) is the point where the line cut across the x axis
Step 2: Find the region that satisfy x + y > 4 i.e the region where the summation of the coordinate is greater than 4
2.1 picking a point to the left of the line e.g (1,1)
x + y = 1+1 = 2
The result 2 does not satisfy the inequalities i.e it is not greater than 4
2.2 picking a point to the right of the line e.g (3,2)
x + y = 3+2 = 5
The result 5 satisfy the inequalities i.e it is greater than 4
Therefore the region to the right of the line x + y = 4 satisfy x + y > 4