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Chapter 4: Q 4.110 (page 464)

Solve the system by graphing. 3x-2y鈮�6y>-14x+5

Short Answer

Expert verified

The solution of the system of the inequality 3x-2y鈮�6y>-14x+5by graphing is the region that contains the point (4,5)

Step by step solution

01

Step 1. Given

The system of inequality is 3x-2y鈮�6y>-14x+5

To solve the inequality by graphing.

02

Step 2. Graph the first inequality

Graph the equation 3x-2y=6for the inequality 3x-2y鈮�6

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

The intercepts are x=2,

y=-3

Since the test point (0,0) makes the inequality true, shade the region that contains the point.

03

Step 3. Graph the second inequality

Graph y>-14x+5by graphing y=-14x+5using the slope m=-14and the y-intercept 5.

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 3x-2y鈮�6y>-14x+5

By testing the point (4,5)on both inequalities,

they hold true.

So the region that contains (4,5)is the solution to both inequalities

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