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Chapter 5: Q.384 (page 682)

In the following exercises, solve each system by graphing

x-y>-1y<13x-2

Short Answer

Expert verified

The solution of the given system using graphing is (6,-2)

Step by step solution

01

Step 1. Given information

We have to find the solution to the given system by using graphing

02

Step 2. Graphing the inequality x-y>-1

Here first, we graph the line x-y=-1and draw a boundary line. we can see that at (0,0) inequality is true, where we have to shade.

Then the graph is given below

03

Step 3. Graph the inequality y<13x-2

Here using slope as m=13and b=-2 we can draw a boundary line and at (0,0) inequality is true, where we have to shade the region.

The graph is given below

04

Step 4. Finding the solution  

The solution is a region where the shading overlaps.

Thus we can take (6,-2 )as a solution checking point, then

Substitutex=6andy=-2inthex-y>-16--2>-16+2>-18>-1,trueputx=6andy=-2iny<13x-2-2<63-2-2<0,trueHerebothinequlitiesaretrueonthepoint(6,-2).So(6,-2)issolution

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