identify the solution set for system of inequalities?

Question

2x+3y<6
y >(or equal to) 1/2*x - 3

Answer 1

Draw the coordinate plane.

Next graph the y >= 1/2*x - 3  inequality boundary with solid line and shade the region with green color.

Then graph the inequality 2x+3y<6 boundary with dotted line and shade the region with pink color.



The solution of 2x+3y<6 is region 2 and 3.

The solution of  y >= 1/2*x - 3 is region 1 and 3.

The region that provides a solution of both inequalities is the solution of the system. Region 2 is the solution of the system.