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WARM UPSolve the following systems of linear equations by any method of your choice.
1. 2.
Infinitely many solutions
No solution
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HOMEWORK ANSWERS12. E; exactly one solution
13. D; no solution
14. F; exactly one solution
15. B; infinitely many solutions
16. A; no solution
17. C; infinitely many solutions
18. no solution
19. infinitely many solutions
20. exactly one solution; (0, -4)
21. infinitely many solutions
22. one solution; (-1, -4)
23. no solution
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7.6 –
GRAPHING
SYSTEM
S OF
LINEA
R
INEQ
UALITI
ES
AL
GE
BR
A 1
( B)
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OBJECTIVES
1. Graph systems of linear inequalities
2. Apply systems of linear inequalities in a real-world context
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SYSTEMS OF INEQUALITIES
Solution of a Linear System of Equations
• Can be determined by graphing, combination, or substitution
• Written as an ordered pair
• Point of intersection of two lines
• Makes all equations in the system true
Solution of a Linear System of Inequalities
Brainstorm with a partner: What does is mean to be a solution of a linear system of equations?
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SYSTEMS OF INEQUALITIES
System of Linear Equations
{2𝑥+3 𝑦=18
𝑦=23𝑥+2
System of Linear Inequalities
{2𝑥+3 𝑦 ≤18
𝑦>23𝑥+2
Systems of linear inequalities have inequality symbols:
Less thanLess than or
equal to Greater than
Greater than or equal to
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SYSTEMS OF INEQUALITIES
Solve the system of inequalities by graphing.
{2𝑥+3 𝑦 ≤18
𝑦>23𝑥+2
1 2 3 4 5 6 7 8 9 10
123
56
4
789
10
-6-4 -2-8
-6
-2
-4
-8
Steps:1. Graph both inequalities (pretend
they are equations).
2. Determine whether the lines should be solid (, ) or dashed (, ).
3. Use test point (usually ) to determine shading.
4. Find overlap in shading. THESE ARE YOUR SOLUTIONS!
5. Check a solution in the double-shaded region!
![Page 8: WARM UP Solve the following systems of linear equations by any method of your choice. Infinitely many solutions No solution](https://reader035.vdocuments.mx/reader035/viewer/2022081603/56649e185503460f94b049ae/html5/thumbnails/8.jpg)
SYSTEMS OF INEQUALITIES
Solve the system of inequalities by graphing.
{ 𝑦<2𝑥≥−1𝑦>𝑥−2
1 2 3 4 5 6 7 8 9 10
123
56
4
789
10
-6-4 -2-8
-6
-2
-4
-8
Steps:1. Graph both inequalities (pretend they
are equations).
2. Determine whether the lines should be solid (, ) or dashed (, ).
3. Use test point (usually to determine shading.
4. Find overlap in shading. THESE ARE YOUR SOLUTIONS!
5. Check a solution in the double-shaded region!
![Page 9: WARM UP Solve the following systems of linear equations by any method of your choice. Infinitely many solutions No solution](https://reader035.vdocuments.mx/reader035/viewer/2022081603/56649e185503460f94b049ae/html5/thumbnails/9.jpg)
BREAK TIMEUse this time to get up, stretch out, talk to a neighbor, or try the following rebus puzzles…
Beaten black and blue
To err on the right side
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SYSTEMS OF INEQUALITIES
Solve the system of inequalities by graphing.
{𝑦<3𝑦 >1
1 2 3 4 5 6 7 8 9 10
123
56
4
789
10
-6-4 -2-8
-6
-2
-4
-8
Steps:1. Graph both inequalities (pretend they are
equations).
2. Determine whether the lines should be solid (, ) or dashed (, ).
3. Use test point (usually to determine shading.
4. Find overlap in shading. THESE ARE YOUR SOLUTIONS!
5. Check a solution in the double-shaded region!
![Page 11: WARM UP Solve the following systems of linear equations by any method of your choice. Infinitely many solutions No solution](https://reader035.vdocuments.mx/reader035/viewer/2022081603/56649e185503460f94b049ae/html5/thumbnails/11.jpg)
SYSTEMS OF INEQUALITIES
Solve the system of inequalities by graphing.
{ 𝑦 ≥ 𝑥−2−𝑥+𝑦<1
1 2 3 4 5 6 7 8 9 10
123
56
4
789
10
-6-4 -2-8
-6
-2
-4
-8
Steps:1. Graph both inequalities (pretend they are
equations).
2. Determine whether the lines should be solid (, ) or dashed (, ).
3. Use test point (usually to determine shading.
4. Find overlap in shading. THESE ARE YOUR SOLUTIONS!
5. Check a solution in the double-shaded region!
![Page 12: WARM UP Solve the following systems of linear equations by any method of your choice. Infinitely many solutions No solution](https://reader035.vdocuments.mx/reader035/viewer/2022081603/56649e185503460f94b049ae/html5/thumbnails/12.jpg)
SYSTEMS OF INEQUALITIES
Solve the system of inequalities by graphing.
{𝑦+1≥ 23𝑥
𝑦<4 𝑥+11 2 3 4 5 6 7 8 9 1
0
123
56
4
789
10
-6-4 -2-8
-6
-2
-4
-8
Steps:1. Graph both inequalities (pretend they are
equations).
2. Determine whether the lines should be solid (, ) or dashed (, ).
3. Use test point (usually to determine shading.
4. Find overlap in shading. THESE ARE YOUR SOLUTIONS!
5. Check a solution in the double-shaded region!
![Page 13: WARM UP Solve the following systems of linear equations by any method of your choice. Infinitely many solutions No solution](https://reader035.vdocuments.mx/reader035/viewer/2022081603/56649e185503460f94b049ae/html5/thumbnails/13.jpg)
EXIT SLIP• Complete the exit slip individually
before leaving today
• You may use your notes or textbook if you want
• When you are done, you may begin the homework assignment
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HOMEWORKDo the following four problems on graph paper by tomorrow!
1. 2. 3.
Graph the system of linear inequalities. Show your work!
4.