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Solve the following system of inequalities graphically.x + y ≥ 4, 2x – y ≤ 0 - Mathematics and Statistics

Graph

Solve the following system of inequalities graphically.
x + y ≥ 4, 2x – y ≤ 0

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Solution

To find graphical solution, construct the table as follows:

Inequation Equation Double Intercept form Points (x, y) Region
x + y ≥ 4 x + y = 4 `"x"/4 + "y"/4` = 1 A (4, 0),
B (0, 4)
0 + 0 `≱ `4
∴ 0 `≱ `4
∴ non-origin side
x – y ≤ 0 2x – y = 0 O (0, 0),
D (2, 4)
2(0) – 0 ≤ 0
∴ 0 ≤ 0
∴ origin side


The shaded portion represents the graphical solution.

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APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 8 Linear Inequations
Miscellaneous Exercise 8 | Q 4 | Page 122
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