Advertisements
Advertisements
Question
Solve the following system of inequalities graphically.
5x + 4y ≤ 20, x ≥ 1, y ≥ 2
Solution
To find graphical solution, construct the table as follows:
| Inequation | Equation | Double Intercept form |
Points (x, y) |
Region |
| 5x + 4y ≤ 20 | 5x + 4y = 20 | `"x"/4 + "y"/5` = 1 | A (4, 0), B (0, 5) |
5(0) + 4(0) ≤ 20 ∴ 0 ≤ 20 ∴ origin side |
| x ≥ 1 | x = 1 | – | – | ∴ 0 `≱` 1 ∴ R.H.S. of line x = 1 |
| y ≥ 2 | y = 2 | – | – | ∴ 0 `≱` 2 ∴ above the line y = 2 |
The shaded portion represents the graphical solution.
APPEARS IN
RELATED QUESTIONS
Solve the inequation:
`("x" - 2)/("x" + 5) > 0`
Solve the following inequation graphically in the two-dimensional plane.
x ≤ – 4
Solve the following inequation graphically in the two-dimensional plane.
y ≥ 3
Solve the following inequations graphically in two-dimensional plane.
y ≤ – 2x
Solve the following inequation graphically in the two-dimensional plane.
x – y ≥ 0
Solve the following inequation graphically in two-dimensional plane.
2x – y ≤ − 2
Solve the following inequation graphically in the two-dimensional plane.
4x + 5y ≤ 40
Mr. Rajesh. Has Rs. 1800 to spend on fruits for a meeting. Grapes cost Rs. 150 per kg. and peaches cost Rs. 200 per kg. Formulate and solve it graphically.
Diet of a sick person must contain at least 4000 units of vitamin. Each unit of food F1 contains 200 units of vitamin, where as each unit of food F2 contains 100 units of vitamins. Write an inequation to fulfil sick person’s requirements and represent the solution set graphically.
Find the graphical solution of the following system of linear inequations:
3x + 2y ≤ 24, 3x + y ≥ 15, x ≥ 4
Solve the following system of inequalities graphically.
x ≥ 3, y ≥ 2
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
Solve the following system of inequalities graphically.
x + y ≤ 9, y > x, x ≥ 0
Solve the following system of inequalities graphically.
x – 2y ≤ 3, 3x + 4y ≥ 12, x ≥ 0, y ≥ 1
Solve the following system of inequalities graphically.
4x + 3y ≤ 60, y ≥ 2x, x ≥ 3, x, y ≥ 0
Solve the following system of inequalities graphically.
x + 2y ≤ 10, x + y ≥ 1, x – y ≤ 0, x ≥ 0, y ≥ 0
