Chapter 3: Q22. (page 147)

22: Solve each system of inequalities by graphing.
$\begin{matrix} |y| > 3 \\ x \leq 1 \end{matrix}$

Short Answer

Expert verified

The solution is $|y| > 3$ and $x \leq 1$ .

Step by step solution

Step-1 – Concept of solution of linear inequalities

The solution of linear inequalities can be obtained by changing the inequalities into equations and solving the linear equations to obtain a graph. Then the common shaded region is a solution of the inequalities.

Step-2 – Concept of shading the region of the inequalities

The shaded region obtained by choosing a point, if the point satisfies the inequality the region is along the point, if not satisfies the inequalities, then the shaded region is opposite to the point.

Step-3 – Evaluation of solution

The two inequalities are $|y| > 3$ and $x \leq 1$ .

The linear inequations of the respective inequalities are $|y| = 3$ and $x = 1$

$y = 3$ or $y = - 3$ , $x = 1$ .

Step-4 – Shading the region

We choose $(0, 0)$ then the point $(0, 0)$ satisfies the inequality $x \leq 1$ but it does not satisfy the inequalities $|y| > 3$ .

Step-5 – Plotting the graph

So, the graph of the inequality is

The common region is $|y| > 3$ and $x \leq 1$

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22: Solve each system of inequalities by graphing.
$\begin{matrix} |y| > 3 \\ x \leq 1 \end{matrix}$

Short Answer

Step by step solution

Step-1 – Concept of solution of linear inequalities

Step-2 – Concept of shading the region of the inequalities

Step-3 – Evaluation of solution

Step-4 – Shading the region

Step-5 – Plotting the graph

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22: Solve each system of inequalities by graphing.y>3x≤1

Short Answer

Step by step solution

Step-1 – Concept of solution of linear inequalities

Step-2 – Concept of shading the region of the inequalities

Step-3 – Evaluation of solution

Step-4 – Shading the region

Step-5 – Plotting the graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Mechanics Maths

Pure Maths

Calculus

Geometry

Applied Mathematics

Study anywhere. Anytime. Across all devices.

22: Solve each system of inequalities by graphing.
$\begin{matrix} |y| > 3 \\ x \leq 1 \end{matrix}$