Theory question 102
InequalitiesShow on a graph, the area which gives the solution set of the inequalities:
y − 2x ≤ 4, 3y + x ≥ 6, y ≥ 7x − 9.
Show the model answer
Model answer
Draw the boundary lines y = 2x + 4 (through (0, 4) and (−2, 0)), x + 3y = 6 (through (0, 2) and (6, 0)) and y = 7x − 9 (through (1, −2) and (2, 5)).
Shade the unwanted side of each line: above y = 2x + 4, below x + 3y = 6, below y = 7x − 9 (or shade the wanted region, stating which).
The solution set is the triangle with vertices about (−0.86, 2.29), (1.5, 1.5) and (2.6, 9.2).
Check with a point inside, e.g. (1, 4): 4 − 2 ≤ 4, 12 + 1 ≥ 6, 4 ≥ −2, all true.
Explanation
Test a point such as (1, 4) in each inequality to know which side to keep.