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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.
Thanks for your help