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Chapter 3: Q1. (page 135)

Solve each system of inequalities by graphing. 1

y-x>0y+x>4

Short Answer

Expert verified

The solution of the inequalities isx<y<4-x.

Step by step solution

01

Step-1 –Concept of solving the linear inequalities

To solve the inequalities we convert the inequalities into linear equations and find the solutions of the equations to obtain the graph.

02

Step-2 –Concept of shading the region

For shading the region, we choose a point. If the point satisfies the inequalities then the shaded region is towards the point otherwise, the shaded region is away from the point.

03

Step-3 –Solving the inequalities

Given inequalities arey-x>0,y+x<4.

Their respective linear equations are y-x=0,y+x=4.

The points which satisfy the equationy-x=0,are 0,0and2,2

The points, which satisfy the equation y+x=40,4and4,0

04

Step-4 –Evaluating the shaded region

We choose1,0to get the shaded region. The point1,0does not satisfy the inequalityy-x=0but it satisfies the inequalityy+x=4

05

Step-5 –Plotting the graph

Therefore, the graph for the inequalities is

The common shaded region isx<y<4-x.

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