Advertisements
Advertisements
प्रश्न
Solve the following systems of inequations graphically:
12x + 12y ≤ 840, 3x + 6y ≤ 300, 8x + 4y ≤ 480, x ≥ 0, y ≥ 0
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: 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 following inequalities and represent the solution graphically on number line:
3x – 7 > 2(x – 6), 6 – x > 11 – 2x
Solve the inequalities and represent the solution graphically on number line:
5(2x – 7) – 3(2x + 3) ≤ 0, 2x + 19 ≤ 6x + 47
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?
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:
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
Show that the solution set of the following linear inequations is empty set:
x + 2y ≤ 3, 3x + 4y ≥ 12, y ≥ 1, x ≥ 0, y ≥ 0
Find the linear inequations for which the solution set is the shaded region given in Fig. 15.42
Show that the solution set of the following linear in equations is an unbounded set:
x + y ≥ 9
3x + y ≥ 12
x ≥ 0, y ≥ 0
Solve the following systems of inequations graphically:
x + 2y ≤ 40, 3x + y ≥ 30, 4x + 3y ≥ 60, x ≥ 0, y ≥ 0
Solve the following systems of inequations graphically:
5x + y ≥ 10, 2x + 2y ≥ 12, x + 4y ≥ 12, 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 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
Solution set of x + y ≥ 0 is
