Advertisements
Advertisements
प्रश्न
Solve the given inequality graphically in two-dimensional plane: –3x + 2y ≥ –6
उत्तर
The graphical representation of – 3x + 2y = – 6 is given in the figure below.
This line divides the xy-plane in two half planes.
Select a point (not on the line), which lies in one of the half planes, to determine whether the point satisfies the given inequality or not.
We select the point as (0, 0).
It is observed that,
– 3(0) + 2(0) ≥ – 6 or 0 ≥ –6, which is true
Therefore, the lower half plane is not the solution region of the given inequality. Also, it is evident that any point on the line satisfies the given inequality.
Thus, the solution region of the given inequality is the half plane containing the point (0, 0) including the line.
The solution region is represented by the shaded region as follows.
APPEARS IN
संबंधित प्रश्न
Solve the given inequality graphically in two-dimensional plane: x + y < 5
Solve the given inequality graphically in two-dimensional plane: 2x + y ≥ 6
Solve the given inequality graphically in two-dimensional plane: 3x + 4y ≤ 12
Solve the given inequality graphically in two-dimensional plane: 2x – 3y > 6
Solve the given inequality graphically in two-dimensional plane: 3y – 5x < 30
Solve the given inequality graphically in two-dimensional plane: y < –2
Solve the given inequality graphically in two-dimensional plane: x > –3
Solve the inequalities and represent the solution graphically on number line:
5x + 1 > –24, 5x – 1 < 24
Solve the following inequalities and represent the solution graphically on number line:
3x – 7 > 2(x – 6), 6 – x > 11 – 2x
How many litres of water will have to be added to 1125 litres of the 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content?
Solve the following systems of linear inequation graphically:
2x + 3y ≤ 6, 3x + 2y ≤ 6, x ≥ 0, y ≥ 0
Solve the following systems of linear inequation graphically:
2x + 3y ≤ 6, x + 4y ≤ 4, x ≥ 0, y ≥ 0
Solve the following systems of linear inequations graphically:
x + y ≥ 1, 7x + 9y ≤ 63, x ≤ 6, y ≤ 5, x ≥ 0, y ≥ 0
Solve the following systems of linear inequations graphically:
2x + 3y ≤ 35, y ≥ 3, x ≥ 2, x ≥ 0, y ≥ 0
Show that the solution set of the following linear inequations is empty set:
x − 2y ≥ 0, 2x − y ≤ −2, x ≥ 0, y ≥ 0
Find the linear inequations for which the solution set is the shaded region given in Fig. 15.42
Solve the following systems of inequations graphically:
2x + y ≥ 8, x + 2y ≥ 8, x + y ≤ 6
Solve the following systems of inequations graphically:
12x + 12y ≤ 840, 3x + 6y ≤ 300, 8x + 4y ≤ 480, x ≥ 0, y ≥ 0
Solve the following systems of inequations graphically:
x + 2y ≤ 40, 3x + y ≥ 30, 4x + 3y ≥ 60, x ≥ 0, y ≥ 0
Show that the following system of linear equations has no solution:
\[x + 2y \leq 3, 3x + 4y \geq 12, x \geq 0, y \geq 1\]
Mark the correct alternative in each of the following:
If x\[<\]7, then
Write the solution of the inequation\[\frac{x^2}{x - 2} > 0\]
State which of the following statement is True or False.
If x < y and b < 0, then `x/"b" < y/"b"`
State which of the following statement is True or False.
If xy > 0, then x > 0 and y < 0
Graph of x < 3 is
Graph of y ≤ 0 is
Solution set of x + y ≥ 0 is
