1 Solving Systems Graphically
1.1 Solving Systems Graphically
Solving Systems Graphically
• Find solution region (or feasible region)
• Will only consider non-strict systems: all inequalities
include ≤ or ≥
• Feasible region is overlap of all half-planes solving
in dividual solutions
Terminology
• A corner point is a point in the solution region on the
intersection of two
(or more) boundary lines
• A solution region is bounded if it can be completely
enclosed in some circle
• Otherwise, it is unbounded
Graphing Linear Inequalities in Two Variables
Problem 1. Graph the solution set of the system of inequalities
y < -3x - 3
y ≥ x + 9
E. N one of the above
Graphing linear inequalities in Two Variables
Problem 2. Graph the solution set of the system of inequalities
x ≤ -4
y > 2
x + y < 5
E. None of the above
Finding Corner Points
Problem 3. Find the coordinates of the corner
points of the solution region for
the system
3x + 2y ≥ 54
4x + 5y ≤ 100
x ≥ 0
y ≥ 0
A. (0, 0), (0, 20), (10, 12), (18, 0)
B. (0, 20), (0, 27), (10, 12)
C. (0, 27), (10, 12), (25, 0)
D. (10, 12), (18, 0), (25, 0)
E. None of the above
Summary
Summary
You should be able to:
• Graph the solution to a system of linear inequalities
• Find the corner points of a solution region
