Advertisements
Advertisements
Question
Find the graphical solution of the following system of linear inequations:
2x + 3y ≥ 12, – x + y ≤ 3, x ≤ 4, y ≥ 3
Solution
The given equations in system are 2x + 3y ≥ 12, – x + y ≤ 3, x ≤ 4, y ≥ 3
Consider the equations:
2x + 3y = 12
| x | 6 | 0 |
| y | 0 | 4 |
The two points on the coordinate axes are (6, 0) and (0, 4).
Origin (0, 0) does not satisfy the inequation as
2(0) + 3(0) ≥ 12
i.e. 0 ≥ 12 which is not true.
∴ Solution set is always from the origin
– x + y = 3
| x | – 3 | 0 |
| y | 0 | 3 |
The points on the coordinate axis are
(− 3, 0) and (0, 3)
Origin (0, 0) satisfies the inequation as
– 0 + 0 ≤ 3 i.e. 0 ≤ 3 which is true.
The solution set is towards the origin.
For x ≤ 4, consider x = 4. Equation of line which passes through the point (4, 0) and since 0 ≤ 4 implies solution is towards the origin.
For y ≥ 3, consider y = 3 which is the equation of a line passing through (0, 3) and parallel to the X-axis.
As 0 ≥ 3 is not possible, the solution set is away from the origin,
The shaded portion represents the graphical solution.
APPEARS IN
RELATED QUESTIONS
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≥ 4, x + y ≤ 3, 2x – 3y ≤ 6
Solve the following system of inequalities graphically: 3x + 2y ≤ 150, x + 4y ≤ 80, x ≤ 15, y ≥ 0, x ≥ 0
Solve the following system of inequalities graphically: x + 2y ≤ 10, x + y ≥ 1, x – y ≤ 0, x ≥ 0, y ≥ 0
The marks scored by Rohit in two tests were 65 and 70. Find the minimum marks he should score in the third test to have an average of at least 65 marks.
A solution is to be kept between 30°C and 35°C. What is the range of temperature in degree Fahrenheit?
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.
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?
The longest side of a triangle is three times the shortest side and third side is 2 cm shorter than the longest side if the perimeter of the triangles at least 61 cm, find the minimum length of the shortest-side.
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 set of values of x satisfying |x − 1| ≤ 3 and |x − 1| ≥ 1.
Write the solution set of the inequation \[\left| \frac{1}{x} - 2 \right| > 4\]
Write the number of integral solutions of \[\frac{x + 2}{x^2 + 1} > \frac{1}{2}\]
Solve each of the following system of equations in R.
\[5x - 7 < 3\left( x + 3 \right), 1 - \frac{3x}{2} \geq x - 4\]
Solve the following system of inequalities graphically.
3x + 2y ≤ 12, x ≥ 1, y ≥ 2
Solve the following system of inequalities graphically.
2x – y ≥ 1, x – 2y ≤ – 1
