Chapter 4: Q. 670 (page 573)

In the following exercises, determine whether each ordered pair is a solution to the given inequality.
Determine whether each ordered pair is a solution to the inequality $y < x - 3$ :
a) $(0, 1)$
b) $(- 2, - 4)$
c) $(5, 2)$
d) $(3, - 1)$
e) $(- 1, - 5)$

Short Answer

Expert verified

The ordered pairs d) $(3, - 1)$ , e) $(- 1, - 5)$ are the solutions to the inequality.

Step by step solution

Step 1. Given information

Given inequality is $y < x - 3$ .

Given ordered pairs are:

a) $(0, 1)$

b) $(- 2, - 4)$

c) $(5, 2)$

d) $(3, - 1)$

e) $(- 1, - 5)$

We have to find the solutions among the given ordered pairs to the given equality.

Step 2. Definition of Solution

An ordered pair $(x, y)$ is a solution of the linear inequality if the pair of values satisfy the inequality when substituted.

Step 3. Substituting the ordered pairs

Substitute the given ordered pairs in the given inequality:

a) $1 < 0 - 3 \Rightarrow 1 < - 2$ False

b) $- 4 < - 2 - 3 \Rightarrow - 4 < - 5$ False

c) $2 < 5 - 3 \Rightarrow 2 < 2$ False

d) $- 1 < 3 - 3 \Rightarrow - 1 < 0$ True

e) $- 5 < - 1 - 3 \Rightarrow - 5 < - 4$ True

Therefore the inequality is true for only ordered pairs c, d, e.

Hence $(3, - 1); (- 1, - 5)$ are solutions among the given ordered pairs.

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In the following exercises, determine whether each ordered pair is a solution to the given inequality.
Determine whether each ordered pair is a solution to the inequality $y < x - 3$ :
a) $(0, 1)$
b) $(- 2, - 4)$
c) $(5, 2)$
d) $(3, - 1)$
e) $(- 1, - 5)$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Definition of Solution

Step 3. Substituting the ordered pairs

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In the following exercises, determine whether each ordered pair is a solution to the given inequality.Determine whether each ordered pair is a solution to the inequality y<x-3:a) (0,1)b) (-2,-4)c) (5,2)d) (3,-1)e)(-1,-5)

Short Answer

Step by step solution

Step 1. Given information

Step 2. Definition of Solution

Step 3. Substituting the ordered pairs

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Mechanics Maths

Applied Mathematics

Geometry

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercises, determine whether each ordered pair is a solution to the given inequality.
Determine whether each ordered pair is a solution to the inequality $y < x - 3$ :
a) $(0, 1)$
b) $(- 2, - 4)$
c) $(5, 2)$
d) $(3, - 1)$
e) $(- 1, - 5)$