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Solve the following system of inequalities graphically.x – 2y ≤ 3, 3x + 4y ≥ 12, x ≥ 0, y ≥ 1 - Mathematics and Statistics

Graph

Solve the following system of inequalities graphically.
x – 2y ≤ 3, 3x + 4y ≥ 12, x ≥ 0, y ≥ 1

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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 ≤ 3 x – 2y = 3

`"x"/3 - (2"y")/3` = 1

i.e., `"x"/3 + "y"/(((-3)/2))` = 1

A (3, 0),
B `(0, (-3)/2)`
0 – 2(0) ≤ 3
∴ 0 ≤ 3
∴ origin side
3x + 4y ≥ 12 3x + 4y = 12 `"x"/4 + "y"/3` = 1 C (4, 0),
D (0, 3)
3(0) + 4(0) `≱` 12
∴ 0 `≱ ` 12
∴ non-origin side
x ≥ 0 x = 0 R.H.S. of Y-axis
y ≥ 1 y = 1 0 `≱`  1
Above the line
y = 1


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 12 | Page 122
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