11th NCERT/CBSE Linear Inequalities Exercise 6.3 Questions 13
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Solve the following system of inequalities graphically:

Question (1)

x > 3 , y > 2

Solution

Question (2)

3x + 2y ≤ 12, x > 1, y > 2

Solution

line l1: 3x + 2y = 12
l2: x = 1; l3: y = 2
 x 0 4 y 6 0

Question (3)

2x + y ≥ 6, 3x +4 y ≥ 12

Solution

line l1: 2x + y = 6
 x 0 3 y 6 0
line l2: 3x +4 y = 12
 x 0 4 y 3 0

Question (4)

x + y ≥ 4. 2x - y > 0

Solution

line l1: x + y = 4
 x 0 4 y 4 0
line l2: 2x - y = 0
 x 0 1 y 0 2

Question (5)

2x - y > 1, x - 2y < -1

Solution

line l1: 2x - y = 1
 x 0 0.5 y -1 0
line l2: x - 2y < 1
 x 0 0.5 y -1 0

Question (6)

x + y ≤ 6, x + y ≥ 4

Solution

line l1: x + y = 6
 x 0 6 y 6 0
line l2: x + y = 4
 x 0 4 y 4 0

Question (7)

2x + y ≥ 8, x + 2y ≥ 10

Solution

line l1: 2x + y = 8
 x 0 4 y 8 0
line l2: x + 2y = 10
 x 0 10 y 5 0

Question (8)

x + y ≤ 9, y > x , x ≥ 0

Solution

line l1: x + y = 9
 x 0 9 y 9 0
line l2: x - y = 0
 x 0 3 y 0 3

Question (9)

5x + 4y ≤ 20, x ≥ 1, y ≥ 2

Solution

line l1: 5x + 4y = 20
 x 0 4 y 5 0

Question (10)

3x + 4y ≤ 60, x + 3y ≤ 30, x ≥ 0, y ≥ 0

Solution

line l1: 3x + 4y = 60
 x 0 20 y 15 0
line l2: x + 3y = 30
 x 0 30 y 10 0

Question (11)

2x +y ≥ 4, x + y ≤ 3, 2x - 3y ≤ 6

Solution

line l1: 2x + y = 4
 x 0 2 y 4 0
line l2: x + y = 3
 x 0 3 y 3 0
line l3: 2x - 3y = 6
 x 0 3 y -2 0

Question (12)

x-2y ≤ 3, 3x+4y ≥ 12, x ≥ 0, y ≥ 1

Solution

line l1: x - 2y = 3
 x 0 3 y -1.5 0
line l2: 3x + 4y = 12
 x 0 4 y 3 0
x = 0 and y = 1

Question (13)

4x+3y≤ 60, y ≥ 2x, x ≥ 3, x, y ≥ 0 line l1: 4x + 3y = 60
 x 0 15 y 20 0
line l2: y - 2x = 0
 x 0 15 y 20 0
line l3: x = 3

Question (14)

3x + 2y ≤ 150, x+ 4y ≤ 80, x ≤ 15, y ≥ 0, x ≥ 0

Solution

line l1: 3x + 2y = 150
 x 0 50 y 75 0
line l2: x + 4y = 80
 x 0 80 y 20 0
line l3: x =15

Question (15)

x + 2y ≤ 10, x + y ≥ 1, x - y ≤ 0, x ≥ 0 , y ≥ 0

Solution

line l1: x + 2y = 10
 x 0 10 y 5 0
line l2: x + y = 1
 x 0 1 y 1 0
line l3: x - y = 0
 x 0 1 y 0 1