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Solve the following system of inequalities graphically.x + 2y ≤ 10, x + y ≥ 1, x – y ≤ 0, x ≥ 0, y ≥ 0 - Mathematics and Statistics

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Sum

Solve the following system of inequalities graphically.
x + 2y ≤ 10, x + y ≥ 1, x – y ≤ 0, x ≥ 0, 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 + 2y ≤ 10 x + 2y = 10 `"x"/10 + "y"/5` = 1 A (10, 0),
B (0, 5)
0 + 2(0) ≤ 10
∴ 0 ≤ 10
∴ origin side
x + y ≥ 1 x + y = 1 `"x"/1 + "y"/1` = 1 C (1, 0),
D (0, 1)
0 + 0 `≱` 1
∴ 0 `≱` 1
∴ non-origin side
x – y ≤ 0 x – y = 0 0 (0, 0),
E(1, 1)
0 – 0 ≤ 0
∴ 0 ≤ 0
∴ origin side
x ≥ 0 x = 0 R.H.S. of Y-axis
y ≥ 0 y = 0 Above X-axis


The shaded portion represents the graphical solution.

Concept: Graphical Solution of Linear Inequality of Two Variable
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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 15 | Page 122
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