Advertisements
Advertisements
प्रश्न
Solve the following system of inequalities graphically.
2x – y ≥ 1, x – 2y ≤ – 1
Advertisements
उत्तर
To find graphical solution, construct the table as follows:
| Inequation | Equation | Double Intercept form |
Points (x, y) |
Region |
| 2x – y ≥ 1 | 2x – y = 1 |
`(2"x")/1 - "y"/1` = 1 i.e., `"x"/(1/2) + "y"/(-1)` = 1 |
A `(1/2, 0)` B (0, – 1) |
2(0) – 0 `≱ ` 1 ∴ 0 `≱ ` 1 ∴ non-origin side |
| x – 2y ≤ – 1 | x – 2y = – 1 |
`"x"/(-1) - (2"y")/(-1)` = 1 i.e., `"x"/(-1) + "y"/((1/2))` = 1 |
C (– 1, 0), D `(0, 1/2)` |
0 – 2(0) `≰ ` – 1 ∴ 0 `≰` – 1 ∴ non-origin side |
The shaded portion represents the graphical solution.
APPEARS IN
संबंधित प्रश्न
Solve the following system of inequalities graphically: x ≥ 3, y ≥ 2
Solve the following system of inequalities graphically: 2x + y≥ 6, 3x + 4y ≤ 12
Solve the following system of inequalities graphically: 2x + y≥ 8, x + 2y ≥ 10
Solve the following system of inequalities graphically: 3x + 4y ≤ 60, x + 3y ≤ 30, x ≥ 0, y ≥ 0
Find all pairs of consecutive odd natural number, both of which are larger than 10, such that their sum is less than 40.
A solution is to be kept between 86° and 95°F. What is the range of temperature in degree Celsius, if the Celsius (C)/ Fahrenheit (F) conversion formula is given by\[F = \frac{9}{5}C + 32\]
To receive grade 'A' in a course, one must obtain an average of 90 marks or more in five papers each of 100 marks. If Shikha scored 87, 95, 92 and 94 marks in first four paper, find the minimum marks that she must score in the last paper to get grade 'A' in the course.
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?
Write the set of values of x satisfying the inequation (x2 − 2x + 1) (x − 4) < 0.
Write the solution set of the equation |2 − x| = x − 2.
Write the number of integral solutions of \[\frac{x + 2}{x^2 + 1} > \frac{1}{2}\]
Write the set of values of x satisfying the inequations 5x + 2 < 3x + 8 and \[\frac{x + 2}{x - 1} < 4\]
Write the solution of set of\[\left| x + \frac{1}{x} \right| > 2\]
Solve each of the following system of equations in R.
\[5x - 7 < 3\left( x + 3 \right), 1 - \frac{3x}{2} \geq x - 4\]
Find the graphical solution of the following system of linear inequations:
3x + 2y ≤ 1800, 2x + 7y ≤ 1400
Find the graphical solution of the following system of linear inequations:
`"x"/60 + "y"/90 ≤ 1`, `"x"/120 + "y"/75 ≤ 1`, y ≥ 0, x ≥ 0
Solve the following system of linear inequalities:
3x + 2y ≥ 24, 3x + y ≤ 15, x ≥ 4
Solution set of x ≥ 0 and y ≤ 0 is
