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Question: Write a system of linear inequalities that defines the shaded region.



A ) y ≤ 3, x ≤ 2 and y > -2
B ) x ≥ -3 and y ≥ -2
C ) x ≥ -3, y < 3, x < 2 and y ≥ -2
D ) None of the above

Steps to derive

1 There are four lines that bound the shaded region. So, the system must have four linear inequalities.

2 Equation of line (1) that passes through the point (-3, 0) is x = -3. The first inequality is bounded by this line.

3 Since the shaded region is on and to the right of the solid boundary line (1), the inequality is x ≥ -3.

4 Equation of line (2) that passes through the point (0, 3) is y = 3. The second inequality is bounded by this line.

5 Since the shaded region is below the dashed boundary line (2), the inequality is y < 3.

6 Equation of line (3) that passes through the point (2, 0) is x = 2. The third inequality is bounded by this line.

7 Since the shaded region is to the left of the dashed boundary line (3), the inequality is x < 2.

8 Equation of line (4) that passes through the point (0, -2) is y = -2. The fourth inequality is bounded by this line.

9 Since the shaded region is on and above the solid boundary line (4), the inequality is y ≥ -2.

10 The system of inequalities that describes the shaded region is x ≥ -3, y < 3, x < 2 and y ≥ -2.



Hence the right answer is Option C

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