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Chapter 4: Q. 403 (page 484)

Solve a System of Linear Inequalities by Graphing
In the following exercises, solve each system by graphing.

x+3y<5y≥-13x+6

Short Answer

Expert verified

There is no solution of the system of the inequality x+3y<5y≥-13x+6since it has no overlapped region.

Step by step solution

01

Step 1. Given

The system of inequality isx+3y<5y≥-13x+6

To find the solution of inequality by graphing

02

Step 2. Graph the first inequality

Graph the line x+3y=5

It is a dashed line since it contains the inequality <.

And test the point (0,0).

It is a solution to the given inequality, so shade the region that contains the point(0,0)

03

Step 3. Graph the second inequality

Graph the line y=-13x+6with slope

m=-13and y-intercept 6

The boundary line is solid line since it contains the inequality≥

Test the inequality with point(0,0)

It is not a solution so shade the region that does not contain the point (0,0)

04

Step 4. Solution of the inequality

From the graph, there is no overlapping region.

So the system of inequality does not contain solution.

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