Solve the following system of inequalities graphically.3x + 2y ≤ 12, x ≥ 1, y ≥ 2 - Mathematics and Statistics

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Graph

Solve the following system of inequalities graphically.
3x + 2y ≤ 12, x ≥ 1, y ≥ 2

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Solution

To find graphical solution, construct the table as follows:

Inequation Equation Double Intercept form Points (x, y) Region
3x + 2y ≤ 12 3x + 2y = 12 `"x"/4 + "y"/6` = 1 A (4, 0),
B (0, 6)
3(0) + 2(0) ≤ 12
∴ 0 ≤ 12
∴ origin side
x ≥ 1 x = 1 0 `≱ ` 1
∴ R.H.S. of line
x = 1
y ≥ 2 y = 2 0 `≱`  2
∴ above line
y = 2


The shaded portion represents the graphical solution.

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Chapter 8: Linear Inequations - Miscellaneous Exercise 8 [Page 122]

APPEARS IN

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

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