Advertisements
Advertisements
Question
Solve the following inequation graphically in two-dimensional plane.
2x – y ≤ − 2
Solution
Consider the equation 2x – y ≤ – 2
∴ corresponding equation is 2x – y = – 2
∴ `(2"x")/-2-"y"/-2=(-2)/-2`
∴ `"x"/-1+"y"/2=1`
∴ intersection of line with X-axis is A (− 1, 0)
intersection of line with Y-axis is B (0, 2)
Origin test:
Substituting x = 0, y = 0 in the given inequation, we get
2(0) – 0 ≤ – 2
0 ≤ – 2
This shows that the origin is not satisfying the inequation.
∴ Points on the non-origin side of the line satisfy the inequation
∴ all the points on the line and above it satisfy the given inequation. The shaded portion represents the solution set.
APPEARS IN
RELATED QUESTIONS
Solve the following inequation graphically in the two-dimensional plane.
y ≥ 3
Solve the following inequations graphically in two-dimensional plane.
y ≤ – 2x
Solve the following inequation graphically in the two-dimensional plane.
y – 5x ≥ 0
Solve the following inequation graphically in the two-dimensional plane.
4x + 5y ≤ 40
Solve the following inequation graphically in the two-dimensional plane.
`1/4 "x" + 1/2 "y" ≤ 1`
Mr. Rajesh. Has Rs. 1800 to spend on fruits for a meeting. Grapes cost Rs. 150 per kg. and peaches cost Rs. 200 per kg. Formulate and solve it graphically.
Solve the following system of inequalities graphically.
x ≥ 3, y ≥ 2
Solve the following system of inequalities graphically.
x + y ≥ 4, 2x – y ≤ 0
Solve the following system of inequalities graphically.
x + y ≤ 6, x + y ≥ 4
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.
3x + 4y ≤ 60, x + 3y ≤ 30, x ≥ 0, y ≥ 0
Solve the following system of inequalities graphically.
x – 2y ≤ 3, 3x + 4y ≥ 12, x ≥ 0, y ≥ 1
Solve the following system of inequalities graphically.
x + 2y ≤ 10, x + y ≥ 1, x – y ≤ 0, x ≥ 0, y ≥ 0
Find the graphical solution of the following system of linear inequations:
0 ≤ x ≤ 350, 0 ≤ y ≤ 150
