Advertisements
Advertisements
Question
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
We have 2x + y ≥ 8, x + 2 y > 10, x ≥ 0, y ≥ 0
Line 2x + y = 8 passes through the points (0, 8) and (4, 0). Line x + 2y = 10 passes through points (10, 0) and (0, 5).
For (0, 0), 2(0) + (0) – 8 < 0, therefore, the region satisfying the inequality 2x+y ≥ 8 And (0, 0) lie on the opposite side of the line 2x +y = 8.
For (0, 0), (0) + 2(0)- 10 <0.
Therefore, the region satisfying the inequality x + 2y≥ 10 And (0, 0) lie on the opposite side of the line x + 2y = 10. Also, for x ≥ 0, y ≥ 0, region lies in the first quadrant.
The common region is plotted as shown in the following figure.
It is clear from the graph that common shaded portion is unbounded.
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: 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: x + y ≤ 9, y > x, x ≥ 0
Solve the following system of inequalities graphically: 3x + 4y ≤ 60, x + 3y ≤ 30, x ≥ 0, y ≥ 0
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
Find all pairs of consecutive odd positive integers, both of which are smaller than 10, such that their sum is more than 11.
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 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 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 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:
`"x"/60 + "y"/90 ≤ 1`, `"x"/120 + "y"/75 ≤ 1`, y ≥ 0, x ≥ 0
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
Find the linear inequalities for which the shaded region in the given figure is the solution set.
Solve the following system of inequalities `(2x + 1)/(7x - 1) > 5, (x + 7)/(x - 8) > 2`
Show that the following system of linear inequalities has no solution x + 2y ≤ 3, 3x + 4y ≥ 12, x ≥ 0, y ≥ 1
Solution set of x ≥ 0 and y ≤ 0 is
