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: 3x + 2y ≤ 12, x ≥ 1, y ≥ 2
Solve the following system of inequalities graphically: 2x + y≥ 6, 3x + 4y ≤ 12
Solve the following system of inequalities graphically: 2x – y > 1, x – 2y < –1
Solve the following system of inequalities graphically: x + y ≤ 6, x + y ≥ 4
Solve the following system of inequalities graphically: 2x + y≥ 8, x + 2y ≥ 10
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 30°C and 35°C. What is the range of temperature in degree Fahrenheit?
Write the set of values of x satisfying |x − 1| ≤ 3 and |x − 1| ≥ 1.
Write the set of values of x satisfying the inequations 5x + 2 < 3x + 8 and \[\frac{x + 2}{x - 1} < 4\]
Write the solution set of the inequation |x − 1| ≥ |x − 3|.
Solve each of the following system of equations in R.
\[5x - 7 < 3\left( x + 3 \right), 1 - \frac{3x}{2} \geq x - 4\]
Solve the following system of inequalities graphically.
3x + 2y ≤ 12, x ≥ 1, y ≥ 2
Solve the following system of inequalities `(2x + 1)/(7x - 1) > 5, (x + 7)/(x - 8) > 2`
Solve the following system of linear inequalities:
3x + 2y ≥ 24, 3x + y ≤ 15, x ≥ 4
Show that the solution set of the following system of linear inequalities is an unbounded region 2x + y ≥ 8, x + 2y ≥ 10, x ≥ 0, y ≥ 0.
Solution set of x ≥ 0 and y ≤ 0 is
Solution set of x ≥ 0 and y ≤ 1 is
