Advertisements
Advertisements
प्रश्न
Solve the following systems of inequations graphically:
12x + 12y ≤ 840, 3x + 6y ≤ 300, 8x + 4y ≤ 480, x ≥ 0, y ≥ 0
Advertisements
उत्तर
Converting the inequations to equations, we obtain:
12x + 12y = 840, 3x + 6y = 300, 8x + 4y = 480, x = 0, y = 0
12x + 12y = 840: This line meets the x-axis at (70, 0) and y-axis at (0, 70). Draw a thick line through these points.
Now, we see that the origin (0, 0) satisfies the inequation 12x + 12y\[\leq\]840
Therefore the region containing the origin is the solution of the inequality 12x + 12y\[\leq\]840
3x + 6y =300: This line meets the x-axis at (100, 0) and y-axis at (0, 50). Draw a thick line through these points.
Now, we see that the origin (0, 0) satisfies the inequation 3x + 6y\[\leq\]300
Therefore, the region containing the origin is the solution of the inequality 3x + 6\[\leq\]300
8x + 4y = 480: This line meets the x-axis at (60, 0) and y-axis at (0, 120). Draw a thick line through these points.
Now, we see that the origin (0, 0) satisfies the inequation 8x + 4y\[\leq\]480 Therefore, the region containing the origin is the solution of the inequality 8x + 4y\[\leq\]480
Also, x\[\geq 0, y \geq 0\]represens the first quadrant. So, the solution set must lie in the first quadrant.
Hence, the solution to the inequalities is the intersection of the above three solutions.
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: –3x + 2y ≥ –6
Solve the given inequality graphically in two-dimensional plane: 3y – 5x < 30
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
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 inequations graphically:
x − y ≤ 1, x + 2y ≤ 8, 2x + y ≥ 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 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 following system of linear equations has no solution:
\[x + 2y \leq 3, 3x + 4y \geq 12, x \geq 0, y \geq 1\]
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\[\frac{x^2}{x - 2} > 0\]
Find the linear inequalities for which the shaded region in the given figure is the solution set.
State which of the following statement is True or False.
If x < y and b < 0, then `x/"b" < y/"b"`
Graph of x ≥ 0 is
Graph of y ≤ 0 is
Solution set of x + y ≥ 0 is
