# 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

#### 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 ≱  1Above the liney = 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