**NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.2**

NCERT Solutions for Class
11 Maths Chapter 6 Linear
Inequalities Ex 6.2 are the part of NCERT Solutions for Class 11 Maths. Here
you can find the NCERT Solutions for Class 11 Maths chapter 6 Linear
Inequalities Ex 6.2.

**Solve the following inequalities graphically in two-dimensional plane.
**

**Ex 6.2 Class 11 Maths Question 1.**

x + y < 5

**Solution.**

We draw the graph of the
equation x + y = 5.

This line passes through the points (0, 5) and (5, 0). The line x + y =
5 is represented by AB. Now, consider the inequality, x + y < 5

Put x = 0, y = 0

0 + 0 = 0 < 5, which is true.

So, the origin O lies in the plane x + y < 5.

∴ The shaded region represents the inequality x + y
< 5.

**Ex 6.2 Class 11 Maths Question
2.**

2x + y ≥ 6

**Solution.**

We draw the graph of the equation 2x + y = 6

The line
passes through the points (0, 6) and (3, 0).

The line 2x
+ y = 6 is represented by AB.

Now,
consider the inequality, 2x + y ≥ 6

Put x = 0,
y = 0

0 + 0 ≥ 6,
which does not satisfy this inequality.

∴ The shaded region represents the inequality 2x + y ≥ 6.

**Ex 6.2 Class 11
Maths Question 3.**

3x + 4y ≤ 12

**Solution.**

We draw the graph of the equation 3x + 4y = 12.

The line passes through the
points (4, 0) and (0, 3). This line is represented by AB.

Now, consider the inequality
3x + 4y ≤ 12.

Putting x = 0, y = 0, we get 0 + 0 = 0 ≤ 12, which is true.

∴ The shaded region represents the
inequality 3x + 4y ≤ 12.

**Ex 6.2 Class 11
Maths Question 4.**

y + 8 ≥ 2x

**Solution.**

Given inequality is y + 8 ≥ 2x.

We draw the graph of the equation y + 8 = 2x

The line passes through the points (4, 0) and (0, -8).

This line is represented by AB.

Now, consider the inequality y + 8 ≥ 2x.

Putting x = 0, y = 0, we get

0 + 8 ≥ 0, which is true.

∴ The shaded region represents the inequality y + 8 ≥ 2x.

**Ex 6.2 Class 11
Maths Question 5.**

x – y ≤ 2

**Solution.**

The given inequality is x – y ≤ 2.

Let us draw the graph of the line x – y = 2.

The line passes through the points (2, 0) and (0, -2).

This line is represented by AB.

Now, consider the inequality x – y ≤ 2.

Putting x = 0, y = 0, we get

0 – 0 ≤ 2, which is true.

∴ Origin lies in the region of x – y ≤ 2.

∴ The shaded region represents the
inequality x – y ≤ 2.

**Ex 6.2 Class 11
Maths Question 6.**

2x – 3y > 6

**Solution.**

Let us draw the graph of line 2x – 3y = 6.

The line passes through the points (3, 0) and (0, -2)

AB represents the equation 2x – 3y = 6.

Now, consider the inequality 2x – 3y > 6.

Putting x = 0, y = 0, we get

0 – 0 > 6, which is not true.

∴ Origin does not lie in the region of 2x
– 3y > 6.

**Ex 6.2 Class 11
Maths Question 7.**

-3x + 2y ≥ -6

**Solution.**

Let us draw the graph of the line -3x + 2y = -6

The line passes through the points (2, 0) and (0, -3).

The line AB represents the equation -3x + 2y = -6.

Now, consider the inequality -3x+ 2y ≥ -6.

Putting x = 0, y = 0, we get

0 + 0 ≥ -6, which is true.

∴ Origin lies in the region of -3x + 2y ≥
-6.

**Ex 6.2 Class 11
Maths Question 8.**

3y – 5x < 30

**Solution.**

The given inequality is 3y – 5x < 30.

Let us draw the graph of the line 3y – 5x = 30.

The line passes through the points (-6, 0) and (0, 10).

The line AB represents the equation 3y – 5x = 30.

Now, consider the inequality 3y – 5x < 30.

Putting x = 0, y = 0, we get

0 – 0 < 30, which is true.

∴ Origin lies in the region of 3y – 5x
< 30.

**Ex 6.2 Class 11
Maths Question 9.**

y < -2

**Solution.**

The given inequality is y < -2

Let us draw the graph of the line y = -2.

The line AB represents the equation y = -2.

Now, consider the inequality
y < -2.

Putting y = 0, we get

0 < -2, which is not true.

∴ Origin does not lie in the region of y
< -2.

The solution region is the shaded region below the line.

Hence, every point below the line (excluding the line) is the solution region.

**Ex 6.2 Class 11
Maths Question 10.**

x > -3

**Solution.**

Let us draw the graph of x = -3.

AB represents the line x = -3.

Now, consider the inequality x > -3.

Putting x = 0, we get, 0 >
-3, which is true.

∴ Origin lies in the region of x > -3.

The graph of the inequality x > -3 is shown in the figure by the shaded region.