Exercise 6.3
Solve the following systems of inequalities graphically:
1. 
Ans. Given:
Putting (0, 0) in 
which is false.
Half plane of 
is away from origin.
Again Putting (0, 0) in 
which is false.
Half plane of 
is away from origin.
2. 
Ans. Given:
Table of values satisfying the equation 
|
|
2 |
4 |
|
|
3 |
0 |
Putting (0, 0) in 
which is true.
Half plane of is towards the origin.
Also, putting (0, 0) in 
which is false.
Half plane of is away from origin.
Again, Again Putting (0, 0) in
which is false.
Half plane of is away from origin.
3. 
Ans. Given:
Table of values satisfying the equation 
|
|
3 |
2 |
|
|
0 |
2 |
Putting (0, 0) in 
which is false.
Half plane of is away from the origin.
Again, Table of values satisfying the equation 
|
|
0 |
4 |
|
|
3 |
0 |
Putting (0, 0) in 
, 
which is true.
Half plane of is towards the origin.
4. 
Ans. Given:
Table of values satisfying the equation 
|
|
3 |
2 |
|
|
1 |
2 |
Putting (0, 0) in 
which is false.
Half plane of 
is away from the origin.
Again, Table of values satisfying the equation 
|
|
1 |
2 |
|
|
2 |
4 |
Putting (3, 0) in 
, 
which is true.
Half plane of is towards the origin.
5. 
Ans. Given:
Table of values satisfying the equation 
|
|
1 |
2 |
|
|
1 |
3 |
Putting (0, 0) in 
which is false.
Half plane of 
is away from the origin.
Again, Table of values satisfying the equation 
|
|
1 |
3 |
|
|
1 |
2 |
Putting (0, 0) in 
which is false.
Half plane of is away from the origin.
6. 
Ans. Given:
Table of values satisfying the equation 
|
|
3 |
4 |
|
|
3 |
2 |
Putting (0, 0) in 
, 
which is true.
Half plane of is towards the origin.
Again, Table of values satisfying the equation
|
|
2 |
1 |
|
|
2 |
3 |
Putting (0, 0) in
which is false.
Half plane of is away from the origin.
7. 
Ans. Given:
Table of values satisfying the equation 
|
|
3 |
4 |
|
|
2 |
0 |
Putting (0, 0) in 
which is false.
Half plane of 
is away from the origin.
Table of values satisfying the equation 
|
|
2 |
1 |
|
|
2 |
3 |
Putting (0, 0) in 
which is false.
Half plane of is away from the origin.
8. 
Ans. Given:
Table of values satisfying the equation 
|
|
5 |
4 |
|
|
4 |
5 |
Putting (0, 0) in 
, 
which is true.
Half plane of is towards the origin.
Table of values satisfying the equation
|
|
3 |
4 |
|
|
3 |
2 |
Putting (0, 0) in ,
which is true.
Half plane of is towards the origin.
9. 
Ans. Given:
Table of values satisfying the equation 
|
|
4 |
0 |
|
|
0 |
5 |
Putting (0, 0) in 
, 
which is true.
Half plane of is towards the origin.
Again, putting (0, 0) in ,
which is false.
Half plane of away from the origin.
Again, putting (0, 0) in ,
which is false.
Half plane of away from the origin.
10. 
Ans. Given:
Table of values satisfying the equation 
|
|
8 |
12 |
|
|
9 |
6 |
Putting (0, 0) in 
which is true.
Half plane of 
is towards the origin.
Table of values satisfying the equation 
|
|
0 |
9 |
|
|
10 |
7 |
Putting (0, 0) in 
which is true.
Half plane of 
is towards the origin.
Again, putting (0, 0) in 
,
which is true.
Half plane of towards the origin.
Again, putting (0, 0) in 
,
which is true.
Half plane of towards the origin.
11. 
Ans. Given:
Table of values satisfying the equation 
|
|
2 |
1 |
|
|
0 |
2 |
Putting (0, 0) in 
which is false.
Half plane of 
is away from the origin.
Table of values satisfying the equation 
|
|
2 |
1 |
|
|
1 |
2 |
Putting (0, 0) in 
which is true.
Half plane of is towards the origin.
Table of values satisfying the equation 
|
|
0 |
3 |
|
|
|
0 |
Putting (0, 0) in 
which is true.
Half plane of 
is towards the origin.
12. 
Ans. Given:
Table of values satisfying the equation 
|
|
1 |
5 |
|
|
|
1 |
Putting (0, 0) in 
which is true.
Half plane of 
is towards the origin.
Table of values satisfying the equation 
|
|
4 |
0 |
|
|
0 |
3 |
Putting (0, 0) in 
which is false.
Half plane of is away from the origin.
Again, putting (0, 0) in ,
which is true.
Half plane of towards the origin.
Again, putting (0, 0) in 
,
which is false.
Half plane of away from the origin.
13. 
Ans. Given:
Table of values satisfying the equation 
|
|
15 |
0 |
|
|
|
20 |
Putting (0, 0) in 
which is true.
Half plane of 
is towards the origin.
Table of values satisfying the equation
|
|
5 |
10 |
|
|
10 |
20 |
Putting (10, 0) in 
which is false.
Half plane of 
is away from the origin.
Again, putting (0, 0) in ,
which is false.
Half plane of away from the origin.
14. 
Ans. Given:
Table of values satisfying the equation 
|
|
30 |
40 |
|
|
3 |
15 |
Putting (0, 0) in 
which is true.
Half plane of is towards the origin.
Table of values satisfying the equation 
|
|
0 |
40 |
|
|
2 |
10 |
Putting (0, 0) in 
which is true.
Half plane of 
is towards the origin.
Again, putting (0, 0) in 
,
which is true.
Half plane of towards the origin.
15. 
Ans. Given:
Table of values satisfying the equation 
|
|
2 |
4 |
|
|
4 |
3 |
Putting (0, 0) in 
which is true.
Half plane of is towards the origin.
Table of values satisfying the equation 
|
|
0 |
1 |
|
|
1 |
0 |
Putting (0, 0) in 
which is false.
Half plane of is away from the origin.
Table of values satisfying the equation 
|
|
1 |
2 |
|
|
1 |
2 |
Putting (2, 0) in 
which is false.
Half plane of 
is away from the origin.
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