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1. SYSTEMS OF LINEAR
INEQUALITIES IN
TWO VARIABLES

2. LEARNING TARGETS

3. LEARNING TARGETS
1. solve a system of linear inequalities in two variables by graphing; and

4. LEARNING TARGETS
1. solve a system of linear inequalities in two variables by graphing; and
2. solve problems involving system of linear inequalities in two variables.

5. Solve the System of Linear Equation

6. Solve the System of Linear Equation
𝑦 ≤ 4𝑥 − 4
5𝑥 − 3𝑦 < 15

7. Solve the System of Linear Equation
𝑦 ≤ 4𝑥 − 4
5𝑥 − 3𝑦 < 15
Solution: Solve for x and y intercept of each inequalities
𝒚 ≤ 𝟒𝒙 − 𝟒 → 𝑦 = 4𝑥 − 4
𝑥 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡
0 = 4𝑥 − 4
−4𝑥 = −4
𝑥 = 1
𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡
𝑦 = 4 0 − 4
𝑦 = 4

8. Solve the System of Linear Equation
𝑦 ≤ 4𝑥 − 4
5𝑥 − 3𝑦 < 15
Solution: Solve for x and y intercept of each inequalities
5𝑥 − 3𝑦 < 15 → 5𝑥 − 3𝑦 = 15
𝑥 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡
5𝑥 − 3 0 = 15
5𝑥 = 15
𝑥 = 3
𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡
5 0 − 3𝑦 = 15
−3𝑦 = 15
𝑦 = −3

9. Solve the System of Linear Equation
𝑦 ≤ 4𝑥 −4 5𝑥 − 3𝑦 < 15

10. Solve the System of Linear Equation
𝑦 ≤ 4𝑥 −4 5𝑥 − 3𝑦 < 15

11. Solve the System of Linear Equation
𝑦 ≤ 4𝑥 − 4
5𝑥 − 3𝑦 < 15

12. Solve the System of Linear Equation
3𝑥 + 4𝑦 > 12
𝑥 ≥ 6𝑦 + 2

13. Solve the System of Linear Equation
3𝑥 + 4𝑦 > 12
𝑥 ≥ 6𝑦 + 2
Solution: Solve for x and y intercept of each inequalities
3𝑥 + 4𝑦 > 12 → 3𝑥 + 4𝑦 = 12
𝑥 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡
3𝑥 + 4y = 4
3𝑥 = 12
𝑥 = 4
𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡
3 0 + 4𝑦 = 12
4𝑦 = 12
𝑦 = 3

14. Solve the System of Linear Equation
3𝑥 + 4𝑦 > 12
𝑥 ≥ 6𝑦 + 2
Solution: Solve for x and y intercept of each inequalities
𝑥 ≥ 6𝑦 + 2 → 𝑥 = 6𝑦 + 2
𝑥 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡
𝑥 = 6 0 + 2
𝑥 = 2
𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡
0 = 6𝑦 + 2
−6𝑦 = 2
𝑦 = −1/3

15. Solve the System of Linear Equation
3𝑥 + 4𝑦 > 12 𝑥 ≥ 6𝑦 + 2

16. Solve the System of Linear Equation
3𝑥 + 4𝑦 > 12 𝑥 ≥ 6𝑦 + 2

17. Solve the System of Linear Equation
3𝑥 + 4𝑦 > 12
𝑥 ≥ 6𝑦 + 2