Advertisements
Advertisements
Question
Find the graphical solution of the following system of linear inequations:
x – y ≤ 0, 2x – y ≥ − 2
Advertisements
Solution
To find graphical solution, construct the table as follows:
| Inequation | Equation | Double Intercept form | Points (x, y) | Region |
| x – y ≤ 0 | x – y = 0 | - | O (0, 0) A (1, 1) |
(0) – (0) ≤ 0 ∴ 0 ≤ 0 ∴ origin side |
| 2x – y ≥ − 2 | 2x – y = − 2 | `(2"x")/-2-"y"/-2=(-2)/-2` | B (–1, 0) C (0, 2) |
2(0) – (0) ≥ –2 ∴ 0 ≥ –2 ∴ origin side |
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: 5x + 4y ≤ 20, x ≥ 1, y ≥ 2
Solve the following system of inequalities graphically: 3x + 4y ≤ 60, x + 3y ≤ 30, x ≥ 0, y ≥ 0
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
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 company manufactures cassettes and its cost and revenue functions for a week are \[C = 300 + \frac{3}{2}x \text{ and } R = 2x\] respectively, where x is the number of cassettes produced and sold in a week. How many cassettes must be sold for the company to realize a profit?
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?
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 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 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
Solve the following system of inequalities `(2x + 1)/(7x - 1) > 5, (x + 7)/(x - 8) > 2`
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 ≤ 1 is
