graphing inequalities

Question

2x-3y is less than or equal to zero 3x+2y is less than or equal to six

 

Answer 1

The system of inequalities are 2x-3y ≤ 0, 3x+2y ≤ 6

Write line equations in the form of y = mx+c

First inequality y = 2/3x

second inequality 3x+2y ≤ 6

y = -(3/2)x+3

Draw a coordinate plane.

Graph the lines  2x-3y = 0  and 3x+2y = 0

The graph of 2x-3y = 0 is solid and included in the graph of solutions and the graph of 3x+2y = 0 is solid and included in the graph of solutions.

The graph of 2x-3y = 0 shaded with fuchsia colour and the graph of 3x+2y = 0 is shaded with teal colour.

the solution of the system is the set of orderd pairs in the intersection of the graph of 2x-3y ≤ 0 and 3x+2y ≤ 6

This region is shaded light purple colour.