Advertisements
Advertisements
प्रश्न
Show that the solution set of the following linear inequations is empty set:
x − 2y ≥ 0, 2x − y ≤ −2, x ≥ 0, y ≥ 0
Advertisements
उत्तर
Converting the inequations to equations, we obtain:
x\[-\]2y = 0, 2x\[-\]y =\[-\]2, x = 0, y = 0
x\[-\] 2y = 0: This line meets the x-axis at (0, 0) and y-axis at (0, 0). If x = 1, then y = 1/2,
so we have another point (1, 1/2). Draw a thick line through (0, 0) and (1, 1/2).
We see that the origin (1, 0) satisfies the inequation x + 2y ≤ 3 So, the portion containing the (1, 0) represents the solution set of the inequation x\[-\]2y ≤ 02x \[-\]y =2: This line meets the x-axis at (\[-\]1, 0) and y-axis at (0, 2). Draw a thick line joining these points.
We see that the origin (0, 0) does not satisfy the inequation 2x \[-\]y\[\leq\]\[-\]y\[\leq\]\[-\]2
Clearly, x ≥ 0, y ≥ 0 represents the first quadrant.
We see in the figure that there is no common region in all the lines. Hence, the solution set to the given set of inequations is empty.
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: y + 8 ≥ 2x
Solve the given inequality graphically in two-dimensional plane: x – y ≤ 2
Solve the given inequality graphically in two-dimensional plane: 2x – 3y > 6
Solve the given inequality graphically in two-dimensional plane: –3x + 2y ≥ –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 inequality and represent the solution graphically on number line:
2(x – 1) < x + 5, 3(x + 2) > 2 – x
A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid. If we have 640 litres of the 8% solution, how many litres of the 2% solution will have to be added?
IQ of a person is given by the formula
IQ = `(MA)/(CA) xx100`
Where MA is mental age and CA is chronological age. If 80 ≤ IQ ≤ 140 for a group of 12 years old children, find the range of their mental age.
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, x + 2y ≤ 8, 2x + y ≥ 2, 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
Find the linear inequations for which the shaded area in Fig. 15.41 is the solution set. Draw the diagram of the solution set of the linear inequations:
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:
x + 2y ≤ 40, 3x + y ≥ 30, 4x + 3y ≥ 60, x ≥ 0, y ≥ 0
Show that the solution set of the following system of linear inequalities is an unbounded region:
\[2x + y \geq 8, x + 2y \geq 10, x \geq 0, y \geq 0\]
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
State which of the following statement is True or False.
If xy > 0, then x < 0 and y < 0
Graph of y ≤ 0 is
