MAT 152: System of Linear Inequalities – Final
(Graphs Matched to Module Samples)
Problem 1
x+y≤6
x − 2y ≥ −4
I. Understand the problem
Graph both inequalities and identify the feasible region (overlap).
II. Make a plan
1. Draw boundary lines: x + y = 6 and x − 2y = −4.
2. Use intercepts: (0,6),(6,0) and (0,2),(−4,0).
3. Shade below x + y = 6 and above x − 2y = −4.
III. Carry out the plan
Boundary lines and intercepts as above. Intersection point is (8/3,10/3).
Sample ordered pairs from the module's answer key: (0,2), (2,2), (4,1), (3,2), (5,1/2).
IV. Look back
The feasible region matches the module: the overlapping shaded triangle bounded by (−4,0),
(8/3,10/3), and (6,0).
Problem 2
4x + 5y ≥ 12
7x + 6y ≤ 42
x≥0
y≥0
I. Understand the problem
Graph the inequalities and find the feasible region restricted to the first quadrant.
II. Make a plan
1. Draw boundary lines: 4x + 5y = 12 and 7x + 6y = 42.
2. Use intercepts: (0,12/5),(3,0) and (0,7),(6,0).
3. Shade above 4x + 5y = 12 and below 7x + 6y = 42, within x ≥ 0,y ≥ 0.
III. Carry out the plan
Feasible region is the trapezoid in the first quadrant bounded by (0,12/5),(0,7),(6,0),(3,0).
Sample ordered pairs from the module's answer key: (1,2),(2,2),(3,2),(0,3),(2,3).
IV. Look back
The feasible region matches the module's sample formation and can be copied directly from the graph
below.