Question 15 - Solving Pair of Linear Inequalities - Chapter 5 Class 11 Linear Inequalities
Last updated at April 16, 2024 by Teachoo
Solving Pair of Linear Inequalities
Question 2 Deleted for CBSE Board 2024 Exams
Question 3 Deleted for CBSE Board 2024 Exams
Question 4 Important Deleted for CBSE Board 2024 Exams
Question 5 Deleted for CBSE Board 2024 Exams
Question 6 Important Deleted for CBSE Board 2024 Exams
Question 7 Important Deleted for CBSE Board 2024 Exams
Question 8 Important Deleted for CBSE Board 2024 Exams
Question 9 Deleted for CBSE Board 2024 Exams
Question 10 Important Deleted for CBSE Board 2024 Exams
Question 11 Important Deleted for CBSE Board 2024 Exams
Question 12 Important Deleted for CBSE Board 2024 Exams
Question 13 Deleted for CBSE Board 2024 Exams
Question 14 Important Deleted for CBSE Board 2024 Exams
Question 15 Important Deleted for CBSE Board 2024 Exams You are here
Solving Pair of Linear Inequalities
Last updated at April 16, 2024 by Teachoo
Question 15 Solve the following system of inequalities graphically: x + 2y ≤ 10, x + y ≥ 1, x – y ≤ 0, x ≥ 0, y ≥ 0 First we solve x + 2y ≤ 10 Lets first draw graph of x + 2y = 10 …(1) Putting x = 0 in (1) 0 + 2y = 10 2y = 10 y = 10/2 y = 5Putting y = 0 in (1) x + 2(0) = 10 x + 0 = 10 x = 10 Points to be plotted are (0,5) , (10,0) Now we solve x + y ≥ 1 Lets first draw graph of x + y = 1 Putting y = 0 in (1) x + 0 = 1 x = 1 Putting x = 0 in (1) 0 + y = 1 y = 1 Points to be plotted are (0,1) , (1,0) Drawing graph Checking for (0,0) Putting x = 0, y = 0 x + y ≥ 1 0 + 0 ≥ 1 0 ≥ 1 which is false Hence origin does not lie in plane x + y ≥ 1 So, we shade right upper side of line Now we solve x – y ≤ 0 Lets first draw graph of x – y = 0 Putting x = 0 in (3) 0 – y = 0 −y = 0 y = 0 Putting y = 2 in (2) x – 2 = 0 x = 0 + 2 x = 2 Points to be plotted are (0,0), (2,2) Drawing graph Checking for (10,0) Putting x = 10, y = 0 x – y ≤ 0 10 – 0 ≤ 0 10 ≤ 0 which is false. Hence (10,0) does not lie in plane x > y So, we shade left side of line Also, given x ≥ 0, y ≥ 0 So, shaded region will lie in first quadrant Hence the shaded region represents the given inequality