Advertisements
Advertisements
Question
Solve the following system of inequalities graphically.
3x + 2y ≤ 12, x ≥ 1, y ≥ 2
Advertisements
Solution
To find graphical solution, construct the table as follows:
| Inequation | Equation | Double Intercept form | Points (x, y) | Region |
| 3x + 2y ≤ 12 | 3x + 2y = 12 | `"x"/4 + "y"/6` = 1 | A (4, 0), B (0, 6) |
3(0) + 2(0) ≤ 12 ∴ 0 ≤ 12 ∴ origin side |
| x ≥ 1 | x = 1 | – | – | 0 `≱ ` 1 ∴ R.H.S. of line x = 1 |
| y ≥ 2 | y = 2 | – | – | 0 `≱` 2 ∴ above line y = 2 |
The shaded portion represents the graphical solution.
APPEARS IN
RELATED QUESTIONS
Solve the following system of inequalities graphically: x ≥ 3, y ≥ 2
Solve the following system of inequalities graphically: 3x + 2y ≤ 12, x ≥ 1, y ≥ 2
Solve the following system of inequalities graphically: x + y≥ 4, 2x – y > 0
Solve the following system of inequalities graphically: 2x – y > 1, x – 2y < –1
Solve the following system of inequalities graphically: 2x + y≥ 8, x + 2y ≥ 10
Solve the following system of inequalities graphically: 5x + 4y ≤ 20, x ≥ 1, y ≥ 2
Solve the following system of inequalities graphically: 2x + y≥ 4, x + y ≤ 3, 2x – 3y ≤ 6
Solve the following system of inequalities graphically: x + 2y ≤ 10, x + y ≥ 1, x – y ≤ 0, x ≥ 0, y ≥ 0
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.
Write the solution set of the inequation \[\left| \frac{1}{x} - 2 \right| > 4\]
Write the solution set of the inequation |x − 1| ≥ |x − 3|.
Solve each of the following system of equations in R.
\[5x - 7 < 3\left( x + 3 \right), 1 - \frac{3x}{2} \geq x - 4\]
Find the graphical solution of the following system of linear inequations:
x – y ≤ 0, 2x – y ≥ − 2
Find the graphical solution of the following system of linear inequations:
2x + 3y ≥ 12, – x + y ≤ 3, x ≤ 4, y ≥ 3
Find the graphical solution of the following system of linear inequations:
3x + 2y ≤ 1800, 2x + 7y ≤ 1400
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
Solution set of x ≥ 0 and y ≤ 0 is
