3.3 Graph Systems of Linear Inequalities. What makes something an inequality? An inequality system x...
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Transcript of 3.3 Graph Systems of Linear Inequalities. What makes something an inequality? An inequality system x...
![Page 1: 3.3 Graph Systems of Linear Inequalities. What makes something an inequality? An inequality system x + y ≤ 8 4x – y > 6.](https://reader036.fdocuments.us/reader036/viewer/2022081520/5697bfae1a28abf838c9c661/html5/thumbnails/1.jpg)
3.3 Graph Systems of Linear Inequalities
![Page 2: 3.3 Graph Systems of Linear Inequalities. What makes something an inequality? An inequality system x + y ≤ 8 4x – y > 6.](https://reader036.fdocuments.us/reader036/viewer/2022081520/5697bfae1a28abf838c9c661/html5/thumbnails/2.jpg)
What makes something an inequality?
• An inequality system
x + y ≤ 8
4x – y > 6
![Page 3: 3.3 Graph Systems of Linear Inequalities. What makes something an inequality? An inequality system x + y ≤ 8 4x – y > 6.](https://reader036.fdocuments.us/reader036/viewer/2022081520/5697bfae1a28abf838c9c661/html5/thumbnails/3.jpg)
Example 1
y > -2x – 5
y ≤ x + 3
![Page 4: 3.3 Graph Systems of Linear Inequalities. What makes something an inequality? An inequality system x + y ≤ 8 4x – y > 6.](https://reader036.fdocuments.us/reader036/viewer/2022081520/5697bfae1a28abf838c9c661/html5/thumbnails/4.jpg)
Extra Example 1
• y ≤ 3x + 2
• y > -x + 4
![Page 5: 3.3 Graph Systems of Linear Inequalities. What makes something an inequality? An inequality system x + y ≤ 8 4x – y > 6.](https://reader036.fdocuments.us/reader036/viewer/2022081520/5697bfae1a28abf838c9c661/html5/thumbnails/5.jpg)
Example 2
2x + 3y < 6
y ≥ -2/3x + 4
![Page 6: 3.3 Graph Systems of Linear Inequalities. What makes something an inequality? An inequality system x + y ≤ 8 4x – y > 6.](https://reader036.fdocuments.us/reader036/viewer/2022081520/5697bfae1a28abf838c9c661/html5/thumbnails/6.jpg)
Example 3
y ≤ 3
y > |x + 4|
![Page 7: 3.3 Graph Systems of Linear Inequalities. What makes something an inequality? An inequality system x + y ≤ 8 4x – y > 6.](https://reader036.fdocuments.us/reader036/viewer/2022081520/5697bfae1a28abf838c9c661/html5/thumbnails/7.jpg)
Guided Practice 1 – 6
![Page 8: 3.3 Graph Systems of Linear Inequalities. What makes something an inequality? An inequality system x + y ≤ 8 4x – y > 6.](https://reader036.fdocuments.us/reader036/viewer/2022081520/5697bfae1a28abf838c9c661/html5/thumbnails/8.jpg)
3 or more inequalities
• Solution to the system is where they all share a shaded area.
![Page 9: 3.3 Graph Systems of Linear Inequalities. What makes something an inequality? An inequality system x + y ≤ 8 4x – y > 6.](https://reader036.fdocuments.us/reader036/viewer/2022081520/5697bfae1a28abf838c9c661/html5/thumbnails/9.jpg)
EXAMPLE 4 Solve a multi-step problem
SHOPPING
A discount shoe store is having a sale, as described in the advertisement shown.
• Use the information in the ad to write a system of inequalities for the regular footwear prices and possible sale prices.• Graph the system of inequalities.
• Use the graph to estimate the range of possible sale prices for footwear that is regularly priced at $70.
![Page 10: 3.3 Graph Systems of Linear Inequalities. What makes something an inequality? An inequality system x + y ≤ 8 4x – y > 6.](https://reader036.fdocuments.us/reader036/viewer/2022081520/5697bfae1a28abf838c9c661/html5/thumbnails/10.jpg)
EXAMPLE 4 Solve a multi-step problem
SOLUTION
STEP 1 Write a system of inequalities. Let x be the regular footwear price and let y be the sale price. From the information in the ad, you can write the following four inequalities.
x ≥ 20 Regular price must be at least $20.
x ≤ 80 Regular price can be at most $80.
y ≥ 0.4x Sale price is at least (100 – 60)% = 40% of regular price.
y ≤ 0.9x Sale price is at most (100 – 10)% = 90% of regular price.
![Page 11: 3.3 Graph Systems of Linear Inequalities. What makes something an inequality? An inequality system x + y ≤ 8 4x – y > 6.](https://reader036.fdocuments.us/reader036/viewer/2022081520/5697bfae1a28abf838c9c661/html5/thumbnails/11.jpg)
EXAMPLE 4 Solve a multi-step problem
STEP 2 Graph each inequality in the system.Then identify the region that is common to all the graphs. It is the region that is shaded.
STEP 3 Identify the range of possible sale prices for $70 footwear. From the graph you can see that when x = 70, the value of y is between these values:
0.4(70) = 28 and 0.9(70) = 63
So, the value of y satisfies 28 ≤ y ≤ 63.
![Page 12: 3.3 Graph Systems of Linear Inequalities. What makes something an inequality? An inequality system x + y ≤ 8 4x – y > 6.](https://reader036.fdocuments.us/reader036/viewer/2022081520/5697bfae1a28abf838c9c661/html5/thumbnails/12.jpg)
Extra Word Problem Example #35
![Page 13: 3.3 Graph Systems of Linear Inequalities. What makes something an inequality? An inequality system x + y ≤ 8 4x – y > 6.](https://reader036.fdocuments.us/reader036/viewer/2022081520/5697bfae1a28abf838c9c661/html5/thumbnails/13.jpg)
Homework
• 1-3, 4 – 16 evens, 17 – 21 odds, 28 – 30, 34, 36, 38
• Bonus: 31 - 33