Graphing and Shading on the tip of your fingernails

3. 2𝑥 − 𝑦 > 3
𝑥 + 2𝑦 ≤ 4
Procedure:
Graph both
equations in the same
Cartesian Plane!

4. 2𝑥 − 𝑦 > 3
2𝑥 − 𝑦 = 3
−𝑦 = −2𝑥 + 3
𝑦 = 2𝑥 − 3
(−1)
2𝑥 − 𝑦 > 32𝑥 − 𝑦 > 3
𝑥 + 2𝑦 ≤ 4
(−1)

5. (0, 0)
2𝑥 − 𝑦 > 3
2𝑥 − 𝑦 > 3
2(0) − (0) > 3
0 − 0 > 3
0 > 3
2𝑥 − 𝑦 > 3
𝑥 + 2𝑦 ≤ 4

6. 𝑥 + 2𝑦 ≤ 4
2𝑥 − 𝑦 > 32𝑥 − 𝑦 > 3
𝑥 + 2𝑦 ≤ 4
𝑥 + 2𝑦 = 4
2𝑦 = −𝑥 + 4
2 2
𝑦 = −
1
2
𝑥 + 2
𝑥 + 2𝑦 ≤ 4

7. (0) + 2(0) ≤ 4
2𝑥 − 𝑦 > 32𝑥 − 𝑦 > 3
𝑥 + 2𝑦 ≤ 4
𝑥 + 2𝑦 ≤ 4
(0, 0)
0 + 0 ≤ 4
0 ≤ 4

8. 2𝑥 − 𝑦 > 32𝑥 − 𝑦 > 3
𝑥 + 2𝑦 ≤ 4
𝑥 + 2𝑦 ≤ 4

9. 2𝑥 − 𝑦 > 32𝑥 − 𝑦 > 3
𝑥 + 2𝑦 ≤ 4
𝑥 + 2𝑦 ≤ 4
(2, −3)
2𝑥 − 𝑦 > 3
2(2) − (−3) > 3
4 − (−3) > 3
4 + 3 > 3
7 > 3
𝑥 + 2𝑦 ≤ 4
2 + 2(−3) ≤ 4
2 − 6 ≤ 4
−4 ≤ 4

10. 𝑦 > −2𝑥 + 3
𝑦 ≥ 𝑥 − 2
𝑦 > −2𝑥 + 3
𝑦 > −2𝑥 + 3
0 > −2(0) + 3
0 > 0 + 3
0 > 3

11. 𝑦 > −2𝑥 + 3
𝑦 ≥ 𝑥 − 2
𝑦 > −2𝑥 + 3
𝑦 ≥ 𝑥 − 2
0 ≥ 0 − 2
0 ≥ −2
𝑦 ≥ 𝑥 − 2

12. 𝑦 > −2𝑥 + 3
𝑦 ≥ 𝑥 − 2
𝑦 > −2𝑥 + 3
𝑦 > −2𝑥 + 3 (1, 3)
3 > −2(1) + 3
3 > −2 + 3
3 > 1
𝑦 ≥ 𝑥 − 2
3 ≥ 1 − 2
3 ≥ −1
𝑦 ≥ 𝑥 − 2

13. Procedure:
1. Graph both equations in the same Cartesian
Plane
2. Solution points are those located in the
overlapping shaded region
3. Check sample solution points on the overlapping
shaded region

15. 𝑦 > −2𝑥 + 3
𝑦 ≥ 𝑥 − 2
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17. Solve this system of linear inequalities by graphing.
Identify a sample solution point. Check this point by
substitution.
𝑦 > −2𝑥 + 3
𝑦 ≥ 𝑥 − 2

18. Try to solve the same system of linear inequalities
algebraically. Use substitution or elimination. Can you
find the solutions? What are the problems and
difficulties you encountered? Do you think you can
solve these systems algebraically? Defend your answer.
𝑦 > −2𝑥 + 3
𝑦 ≥ 𝑥 − 2