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Chapter 5: Q. 388 (page 682)

In the following exercises, solve each system by graphing.

y鈮�2x鈭�5鈭�6x+3y>鈭�4

Short Answer

Expert verified

The solution is the area shaded twice which is the darker-shaded region.

Step by step solution

01

Step 1. Given Information

In the given exercises we have to solve given system by graphing.

y鈮�2x鈭�5鈭�6x+3y>鈭�4

02

Step 2. Graph y≥2x−5, by graphing y=2x−5 using the slope m=2 and the y-intercept b=-5. 

Test (0,0). It makes the inequality false. So, shade the side that contains (0,0)blue.

03

Step 2. Graph −6x+3y>−4, by graphing −6x+3y=−4 and testing a point.

Divide by 鈭�4on both side

鈭�6鈭�4x+3鈭�4y=鈭�4鈭�432x-34y=1

The intercepts are x=32andy=-34and the boundary line will be dashed.

04

Step 3. Test (0,0). It makes the inequality true. So, shade the side that contain (0,0) red. 

05

Step 5. The point (0,0) is in the solution and we have already found it to be a solution of each inequality. 

The point of intersection of the two lines is included.

The solution is the area shaded twice which is the darker-shaded region.

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