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 + 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: x + y ≤ 6, x + y ≥ 4
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 ≤ 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: 3x + 2y ≤ 150, x + 4y ≤ 80, x ≤ 15, y ≥ 0, x ≥ 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\[F = \frac{9}{5}C + 32\]
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 there are 640 litres of the 8% solution, how many litres of 2% solution will have to be added?
The water acidity in a pool is considered normal when the average pH reading of three daily measurements is between 7.2 and 7.8. If the first two pH reading are 7.48 and 7.85, find the range of pH value for the third reading that will result in the acidity level being normal.
Write the solution set of the equation |2 − x| = x − 2.
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:
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
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 inequalities graphically.
2x – y ≥ 1, x – 2y ≤ – 1
Solve the following system of linear inequalities:
3x + 2y ≥ 24, 3x + y ≤ 15, x ≥ 4
