Chapter 3: Q1. (page 135)

Solve each system of inequalities by graphing. 1
$\begin{array}{l} y - x > 0 \\ y + x > 4 \end{array}$

Short Answer

Expert verified

The solution of the inequalities is $x < y < 4 - x .$

Step by step solution

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.

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.

Step-3 –Solving the inequalities

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

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

The points which satisfy the equation $y - x = 0,$ are $(0, 0)$ and $(2, 2)$

The points, which satisfy the equation $y + x = 4$ $(0, 4)$ and $(4, 0)$

Step-4 –Evaluating the shaded region

We choose $(1, 0)$ to get the shaded region. The point $(1, 0)$ does not satisfy the inequality $y - x = 0$ but it satisfies the inequality $y + x = 4$

Step-5 –Plotting the graph

Therefore, the graph for the inequalities is

The common shaded region is $x < y < 4 - x .$

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Solve each system of inequalities by graphing. 1
$\begin{array}{l} y - x > 0 \\ y + x > 4 \end{array}$

Short Answer

Step by step solution

Step-1 –Concept of solving the linear inequalities

Step-2 –Concept of shading the region

Step-3 –Solving the inequalities

Step-4 –Evaluating the shaded region

Step-5 –Plotting the graph

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Solve each system of inequalities by graphing. 1y-x>0y+x>4

Short Answer

Step by step solution

Step-1 –Concept of solving the linear inequalities

Step-2 –Concept of shading the region

Step-3 –Solving the inequalities

Step-4 –Evaluating the shaded region

Step-5 –Plotting the graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Theoretical and Mathematical Physics

Discrete Mathematics

Pure Maths

Geometry

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Solve each system of inequalities by graphing. 1
$\begin{array}{l} y - x > 0 \\ y + x > 4 \end{array}$