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SYSTEMS OF LINEAR
INEQUALITIES IN
TWO VARIABLES
LEARNING TARGETS
LEARNING TARGETS
1. solve a system of linear inequalities in two variables by graphing; and
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.
Solve the System of Linear Equation
Solve the System of Linear Equation
𝑦 ≤ 4𝑥 − 4
5𝑥 − 3𝑦 < 15
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
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
Solve the System of Linear Equation
𝑦 ≤ 4𝑥 −4 5𝑥 − 3𝑦 < 15
Solve the System of Linear Equation
𝑦 ≤ 4𝑥 −4 5𝑥 − 3𝑦 < 15
Solve the System of Linear Equation
𝑦 ≤ 4𝑥 − 4
5𝑥 − 3𝑦 < 15
Solve the System of Linear Equation
3𝑥 + 4𝑦 > 12
𝑥 ≥ 6𝑦 + 2
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
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
Solve the System of Linear Equation
3𝑥 + 4𝑦 > 12 𝑥 ≥ 6𝑦 + 2
Solve the System of Linear Equation
3𝑥 + 4𝑦 > 12 𝑥 ≥ 6𝑦 + 2
Solve the System of Linear Equation
3𝑥 + 4𝑦 > 12
𝑥 ≥ 6𝑦 + 2

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SYSTEMS-OF-LINEAR-INEQUALITIES-IN-TWO-VARIABLES.pptx

  • 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