Question 1
Solve the inequality x + y ≤ 5 graphically in two dimensional plane.
Sol:
The given inequality x + y ≤ 5 is graphically represented with the help of the blue line which divides the Cartesian plane into two parts, that is I and II, respectively.
Select a point a in any one of the parts but not on the line to determine whether the point satisfies the given inequality or not.
Let us consider the point be O (0, 0)
Putting the values of x and y in the given inequality. We have:
= 0 + 0 ˂ 5
= 0 ˂ 5
This is true.
Therefore, plane II is not the graphical solution of the given inequality. Also, if we take any point on the line it will not satisfy the given inequality.
Thus the feasible solution of the given inequality is the shaded portion of the in the Cartesian plane excluding the points on the line and that is plane I.
Graphical representation:
Question 2
Solve the inequality 2x + y ≥ 5 graphically in two dimensional plane.
Sol:
The given inequality 2x + y ≥ 5 is graphically represented with the help of the blue line which divides the Cartesian plane into two parts that, is I and II, respectively.
Select a point a in any one of the parts but not on the line to determine whether the point satisfies the given inequality or not.
Let us consider the point be O (0, 0)
Putting the values of x and y in the given inequality. We have:
= 2(0) + 0 ≥ 6
= 0 ≥ 6
This is false.
Therefore, plane I is not the graphical solution of the given inequality. Also, if we take any point on the line it will not satisfy the given inequality.
Thus the feasible solution of the given inequality is the shaded portion of the in the Cartesian plane excluding the points on the line and that is plane II.
Graphical representation:
Question 3
Solve the inequality 3x+4y ≤ 12 graphically in two dimensional plane.
Sol:
The given inequality 3x + 4y ≤ 12 is graphically represented with the help of the blue line which divides the Cartesian plane into two parts, that is, I and II respectively.
Select a point a in any one of the parts but not on the line to determine whether the point satisfies the given inequality or not.
Let us consider the point be O (0, 0)
Putting the values of x and y in the given inequality. We have:
= 3(0) + 4(0) ≤ 12
= 0 ≤ 12
This is true.
Therefore, plane II is not the graphical solution of the given inequality. Also, if we take any point on the line it will not satisfy the given inequality.
Thus the feasible solution of the given inequality is the shaded portion of the in the Cartesian plane excluding the points on the line and that is plane I.
Graphical representation:
Question 4
Solve the inequality y+8 ≥ 2x graphically in two dimensional plane.
Sol:
The given inequality y+8 ≥ 2x is graphically represented with the help of the blue line which divides the Cartesian plane into two parts that is, I and II, respectively.
Select a point a in any one of the parts but not on the line to determine whether the point satisfies the given inequality or not.
Let us consider the point be O (0, 0)
Putting the values of x and y in the given inequality. We have:
= (0) + (8) ≥ 2(0)
= 8 ≥ 0
This is true.
Therefore, plane II is not the graphical solution of the given inequality. Also, if we take any point on the line it will not satisfy the given inequality.
Thus the feasible solution of the given inequality is the shaded portion of the in the Cartesian plane excluding the points on the line and that is plane I.
Graphical representation:
Question 5
Solve the inequality x-y ≤ 2 graphically in two dimensional plane.
Sol:
The given inequality x-y ≤ 2 is graphically represented with the help of the blue line which divides the Cartesian plane into two parts that is, I and II, respectively.
Select a point a in any one of the parts but not on the line to determine whether the point satisfies the given inequality or not.
Let us consider the point be O (0, 0)
Putting the values of x and y in the given inequality. We have:
= 0 – 0 ≤ 2
= 0 ≤ 2
This is true.
Therefore, lower half of the plane is not the graphical solution of the given inequality. Also, if we take any point on the line it will not satisfy the given inequality.
Thus the feasible solution of the given inequality is the shaded portion of the in the Cartesian plane excluding the points on the line and that is plane I.
Graphical representation:
Question 6
Solve the inequality 2x – 3y ˃ 6 graphically in two dimensional plane.
Sol:
The given inequality 2x – 3y ˃ 6 is graphically represented with the help of the blue line which divides the Cartesian plane into two parts, that is, I and II respectively.
Select a point a in any one of the parts but not on the line to determine whether the point satisfies the given inequality or not.
Let us consider the point be O (0, 0)
Putting the values of x and y in the given inequality. We have:
=2(0) – 3(0) ≥ 6
= 0 ≥ 6
This is false.
Therefore, the upper part of the plane is not the graphical solution of the given inequality. Also, if we take any point on the line it will not satisfy the given inequality.
Thus the feasible solution of the given inequality is the shaded portion of the in the Cartesian plane excluding the points on the line and that is plane II.
Graphical representation:
Question 7
Solve the inequality -3x + 2y ≥ -6 graphically in two dimensional plane.
Sol:
The given inequality -3x + 2y ≥ -6 is graphically represented with the help of the blue line which divides the Cartesian plane into two parts that is, I and II, respectively.
Select a point a in any one of the parts but not on the line to determine whether the point satisfies the given inequality or not.
Let us consider the point be O (0, 0)
Putting the values of x and y in the given inequality. We have:
=-3(0) + 2(0) ≥ -6
= 0 ≥ -6
This is true.
Therefore, the lower part of the plane is not the graphical solution of the given inequality. Also, if we take any point on the line it will not satisfy the given inequality.
Thus the feasible solution of the given inequality is the shaded portion of the in the Cartesian plane excluding the points on the line and that is plane II.
Graphical representation:
Question 8
Solve the inequality 3y – 5x ˂ 30 graphically in two dimensional plane.
Sol:
The given inequality 3y – 5x ˂ 30 is graphically represented with the help of the blue line which divides the Cartesian plane into two parts that is, I and II, respectively.
Select a point a in any one of the parts but not on the line to determine whether the point satisfies the given inequality or not.
Let us consider the point be O (0, 0)
Putting the values of x and y in the given inequality. We have:
=3(0) – 5(0) ˂ 30
= 0 ˂ 30
This is true.
Therefore, the upper part of the plane is not the graphical solution of the given inequality. Also, if we take any point on the line it will not satisfy the given inequality.
Thus the feasible solution of the given inequality is the shaded portion of the in the Cartesian plane excluding the points on the line and that is plane II.
Graphical representation:
Question 9
Solve the inequality y ˂ -2 graphically in two dimensional plane.
Sol:
The given inequality y ˂ -2 is graphically represented with the help of the blue line which divides the Cartesian plane into two parts that is, I and II, respectively.
Select a point a in any one of the parts but not on the line to determine whether the point satisfies the given inequality or not.
Let us consider the point be O (0, 0)
Putting the values of x and y in the given inequality. We have:
= (0) ˂ -2
This is false.
Therefore, the upper part of the plane is not the graphical solution of the given inequality. Also, if we take any point on the line it will not satisfy the given inequality.
Thus the feasible solution of the given inequality is the shaded portion of the in the Cartesian plane excluding the points on the line and that is plane II.
Graphical representation:
Question 10
Solve the inequality x ˃ -3 graphically in two dimensional plane.
Sol:
The given inequality x ˃ -3 is graphically represented with the help of the blue line which divides the Cartesian plane into two parts that is, I and II, respectively.
Select a point a in any one of the parts but not on the line to determine whether the point satisfies the given inequality or not.
Let us consider the point be O (0, 0)
Putting the values of x and y in the given inequality. We have:
= (0) ˂ -3
= 0 ˂ -3
This is true
Therefore, the upper part of the plane is not the graphical solution of the given inequality. Also, if we take any point on the line it will not satisfy the given inequality.
Thus the feasible solution of the given inequality is the shaded portion of the in the Cartesian plane excluding the points on the line and that is plane II.
Graphical representation:
