Chapter 3: Q23. (page 147)

23: Solve each system of inequalities by graphing.
$\begin{matrix} y < x + 1 \\ x > 5 \end{matrix}$

Short Answer

Expert verified

The solution is $y < x + 1$ .

Step by step solution

Step-1 – Concept of solution of linear inequalities

The solution of the inequalities can be obtained by changing the inequalities into equations and solving the linear equations.

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 $y < x + 1$ and $x > 5$ .

The linear inequation of the respective inequalities are $y = x + 1$ and $x = 5$ .

Point which satisfies the equation $y = x + 1$ are $(0, 1)$ and $(- 1, 0)$ .

Step-4 – Shading the region

We choose $(0, 0)$ then the point $(0, 0)$ satisfies the inequality $y < x + 1$ but the point does not satisfy the inequality $x > 5$ .

Step-5 – Plotting the graph

So, the graph of the inequality is

The common region is $y < x + 1$ .

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23: Solve each system of inequalities by graphing.
$\begin{matrix} y < x + 1 \\ x > 5 \end{matrix}$

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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23: Solve each system of inequalities by graphing.y<x+1x>5

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

Probability and Statistics

Pure Maths

Mechanics Maths

Logic and Functions

Calculus

Geometry

Study anywhere. Anytime. Across all devices.

23: Solve each system of inequalities by graphing.
$\begin{matrix} y < x + 1 \\ x > 5 \end{matrix}$