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Chapter 4: Q 4.109 (page 464)

Solve the system by graphing. x+y≤2y≥23x-1

Short Answer

Expert verified

The solution of the system of the inequality x+y≤2y≥23x-1by graphing is the region that contains the point (0,0)

Step by step solution

01

Step 1. Given

The system of inequalityx+y≤2y≥23x-1

To solve the inequality by graphing.

02

Step 2. Graph the first inequality

Graph the equation x+y=2for the inequality x+y≤2

And test the point (0,0)and it holds true.

The intercepts are x=2

y=2

Test the point (0,0)which makes the inequality true. So shade the region that contains the point

(0,0)

03

Step 3. Graph the second inequality

Graph y≥23x-1by graphing y=23x-1using the slope y=23and y-intercept 1.

The boundary line is solid.

Test (0,0) which makes the inequality true, so
shade the side that contains (0,0).

04

Step 4. Test the inequalities with point (0,0)

x+y≤2y≥23x-1

By testing the point (0,0)on both the inequalities, they hold true.

So the region that contains (0,0) is the solution to both inequalities

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