Graphical solutions of systems of linear inequalities in two variables
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Transcript of Graphical solutions of systems of linear inequalities in two variables
Good Morning Class
GRAPHICAL SOLUTIONS OF SYSTEMS OF LINEAR
INEQUALITIES IN TWO VARIABLES
2 π₯β π¦>3π₯+2 π¦ β€4
Procedure:
Graph both equations in the same Cartesian Plane!
2 π₯β π¦>32 π₯β π¦=3β π¦=β2π₯+3π¦=2 π₯β3
(β1)
2 π₯β π¦>32 π₯β π¦>3π₯+2 π¦ β€4
(β1)
(0 ,0)2 π₯β π¦>3
2 π₯β π¦>3
2(0)β(0)>30β0>30>3
2 π₯β π¦>3π₯+2 π¦ β€4
π₯+2 π¦ β€4
2 π₯β π¦>32 π₯β π¦>3π₯+2 π¦ β€4
π₯+2 π¦=42 π¦=βπ₯+42 2π¦=β 12 π₯+2
π₯+2 π¦ β€4
(0)+2(0)β€4
2 π₯β π¦>32 π₯β π¦>3π₯+2 π¦ β€4
π₯+2 π¦ β€4(0 ,0)
0+0β€ 40β€ 4
2 π₯β π¦>32 π₯β π¦>3π₯+2 π¦ β€4
π₯+2 π¦ β€4
2 π₯β π¦>32 π₯β π¦>3π₯+2 π¦ β€4
π₯+2 π¦ β€4(2 ,β3)
2 π₯β π¦>32(2)β(β3)>34β(β3)>34+3>37>3
π₯+2 π¦ β€42+2 (β3)β€42β6 β€4β4β€ 4
π¦>β2 π₯+3π¦ β₯ π₯β2
π¦>β2 π₯+3
π¦>β2 π₯+30>β2(0)+30>0+30>3
π¦>β2 π₯+3π¦ β₯ π₯β2
π¦>β2 π₯+3
π¦ β₯ π₯β20β₯0β20β₯β2
π¦ β₯ π₯β2
π¦>β2 π₯+3π¦ β₯ π₯β2
π¦>β2 π₯+3
π¦>β2 π₯+3 (1 ,3)3>β2(1)+33>β2+33>1
π¦ β₯ π₯β23β₯1β23β₯β1
π¦ β₯ π₯β2
Procedure:
1. Graph both equations in the same Cartesian Plane
2. Solution points are those located in the overlapping shaded region
3. Check sample solution points on the overlapping shaded region
GRAPHICAL SOLUTIONS OF SYSTEMS OF LINEAR
INEQUALITIES IN TWO VARIABLES
π¦>β2 π₯+3π¦ β₯ π₯β2
Find out who are my favorite students!
QUIZ
Solve this system of linear inequalities by graphing. Identify a sample solution point. Check this point by substitution.
π¦>β2 π₯+3π¦ β₯ π₯β2
ASSIGNMENT
Try to solve the same system of linear inequalities algebraically. Use substitution or elimination. Can you find the solutions? What are the problems and difficulties you encountered? Do you think you can solve these systems algebraically? Defend your answer.π¦>β2 π₯+3
π¦ β₯ π₯β2
Thank You