4.3.1 – Systems of Inequalities. Recall, we solved systems of equations What defined a system? How...
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Transcript of 4.3.1 – Systems of Inequalities. Recall, we solved systems of equations What defined a system? How...
![Page 1: 4.3.1 – Systems of Inequalities. Recall, we solved systems of equations What defined a system? How did you find the solutions to the system?](https://reader036.fdocuments.us/reader036/viewer/2022072009/56649d995503460f94a83c43/html5/thumbnails/1.jpg)
4.3.1 – Systems of Inequalities
![Page 2: 4.3.1 – Systems of Inequalities. Recall, we solved systems of equations What defined a system? How did you find the solutions to the system?](https://reader036.fdocuments.us/reader036/viewer/2022072009/56649d995503460f94a83c43/html5/thumbnails/2.jpg)
• Recall, we solved systems of equations
• What defined a system?
• How did you find the solutions to the system?
![Page 3: 4.3.1 – Systems of Inequalities. Recall, we solved systems of equations What defined a system? How did you find the solutions to the system?](https://reader036.fdocuments.us/reader036/viewer/2022072009/56649d995503460f94a83c43/html5/thumbnails/3.jpg)
Systems of Inequalities
• A system of linear inequalities has 2 or more linear inequalities
• Their solutions are any ordered pair that satisfies BOTH inequalities
• Only method to solve? Graphing
![Page 4: 4.3.1 – Systems of Inequalities. Recall, we solved systems of equations What defined a system? How did you find the solutions to the system?](https://reader036.fdocuments.us/reader036/viewer/2022072009/56649d995503460f94a83c43/html5/thumbnails/4.jpg)
Solutions
• To test whether a particular solution, or solution set (x,y) is a solution, we plug the x and y solutions and test both inequalities
• Example. Check whether (3, -1) is a solution to the system:
• x + y > 1• y < 2
![Page 5: 4.3.1 – Systems of Inequalities. Recall, we solved systems of equations What defined a system? How did you find the solutions to the system?](https://reader036.fdocuments.us/reader036/viewer/2022072009/56649d995503460f94a83c43/html5/thumbnails/5.jpg)
• Example. Tell whether (4, 2) is a solution to the system:
• x + y ≤ 2• 4x – y > 3
![Page 6: 4.3.1 – Systems of Inequalities. Recall, we solved systems of equations What defined a system? How did you find the solutions to the system?](https://reader036.fdocuments.us/reader036/viewer/2022072009/56649d995503460f94a83c43/html5/thumbnails/6.jpg)
• Example. Tell whether (4, 2) is a solution to the system:
• x > 1• x + y ≤ 4
![Page 7: 4.3.1 – Systems of Inequalities. Recall, we solved systems of equations What defined a system? How did you find the solutions to the system?](https://reader036.fdocuments.us/reader036/viewer/2022072009/56649d995503460f94a83c43/html5/thumbnails/7.jpg)
Solving Systems
• Similar to solving equations, to solve a linear system, we will graph both inequalities on the same plane
• Remember…• <, > = Dashed Line• ≤, ≥ = Solid Line• >, ≥ = Shade Above (when not in std. form)• <, ≤ = Shade Below (when not in std. form)
![Page 8: 4.3.1 – Systems of Inequalities. Recall, we solved systems of equations What defined a system? How did you find the solutions to the system?](https://reader036.fdocuments.us/reader036/viewer/2022072009/56649d995503460f94a83c43/html5/thumbnails/8.jpg)
• Solutions?
• The solutions are where the shading will overlap
• Helpful to have 2 colors
• To check your solution, choose a test point in the overlapping shaded region
![Page 9: 4.3.1 – Systems of Inequalities. Recall, we solved systems of equations What defined a system? How did you find the solutions to the system?](https://reader036.fdocuments.us/reader036/viewer/2022072009/56649d995503460f94a83c43/html5/thumbnails/9.jpg)
• Example. Find the solutions to the system• y < 2x – 3• y ≥ -x - 1
![Page 10: 4.3.1 – Systems of Inequalities. Recall, we solved systems of equations What defined a system? How did you find the solutions to the system?](https://reader036.fdocuments.us/reader036/viewer/2022072009/56649d995503460f94a83c43/html5/thumbnails/10.jpg)
• Example. Find the solutions to the system• y ≤ x - 4• x ≥ -8
![Page 11: 4.3.1 – Systems of Inequalities. Recall, we solved systems of equations What defined a system? How did you find the solutions to the system?](https://reader036.fdocuments.us/reader036/viewer/2022072009/56649d995503460f94a83c43/html5/thumbnails/11.jpg)
• Example. Find the solutions to the system• y ≤ -x + 5• x – y < 4
![Page 12: 4.3.1 – Systems of Inequalities. Recall, we solved systems of equations What defined a system? How did you find the solutions to the system?](https://reader036.fdocuments.us/reader036/viewer/2022072009/56649d995503460f94a83c43/html5/thumbnails/12.jpg)
• Example. Find the solutions to the system• x + y > 4• 2x – y ≥ 3
![Page 13: 4.3.1 – Systems of Inequalities. Recall, we solved systems of equations What defined a system? How did you find the solutions to the system?](https://reader036.fdocuments.us/reader036/viewer/2022072009/56649d995503460f94a83c43/html5/thumbnails/13.jpg)
• Assignment• Pg. 188• 3-8 all, 10-18 even