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Chapter 4: Q 4.111 (page 465)

Solve the system by graphing. y鈮�3x-2y<-1

Short Answer

Expert verified

The solution is the area shaded twice鈥攚hich appears as the darkest shaded region which contains the point (0,-2)

Step by step solution

01

Step 1. Given

The system of inequality y鈮�3x-2y<-1

To find the solution by graphing

02

Step 2. Graph the first inequality

Graph y鈮�3x-2by graphing y=3x-2and the intercepts are x=23,

y=-1

Test a point (0,0).

And it holds true. So shade the region that contains the inequality.

03

Step 3. Graph the second inequality

Graph y<-1by graphing y=-1.

It is a horizontal line through y=-1and the boundary line will be dashed.

Test (0,0)that makes the inequality false.

So shade the region that does not contain the test point.

04

Step 4.Test the inequalities with point in the overlapped region 

The system of inequality is y鈮�3x-2y<-1

Test the point (0,-2)and it holds true for both the region.

So the overlapped region that contains (0,-2) is the solution to the system.

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