Q. 278 In the following exercises, dete... [FREE SOLUTION]

91影视

Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 5: Q. 278 (page 672)

In the following exercises, determine whether each ordered pair is a solution to the system.
$\{\begin{cases} y < \frac{3}{2} x + 3 \\ \frac{3}{4} x - 2 y < 5 \end{cases} a . (- 4, - 1) b . (8, 3)$

Short Answer

Expert verified

Part (a) The ordered pair is not a solution to the set.

Part (b) The ordered pair is a solution to the set.

Step by step solution

Part a. Step 1. Given Information

The given set is $\{\begin{cases} y < \frac{3}{2} x + 3 \\ \frac{3}{4} x - 2 y < 5 \end{cases}$ and the ordered pair is $(- 4, - 1)$ .

Part a. Step 2. Substitute the values into the inequalities.

Substitute $x = - 4, y = - 1$ into the first given inequality.

$- 1 \overset{?}{<} \frac{3}{2} (- 4) + 3 - 1 \overset{?}{<} - 6 + 3 - 1 < - 3 f a l s e$

Substitute $x = - 4, y = - 1$ into the second inequality.

$\frac{3}{4} (- 4) - 2 (- 1) \overset{?}{<} 5 - 3 + 2 \overset{?}{<} 5 - 1 < 5 t r u e$

Since the first inequality is not satisfied, the given ordered pair is not a solution to the system.

Part b. Step 1. Given Information

The given set is $\{\begin{cases} y < \frac{3}{2} x + 3 \\ \frac{3}{4} x - 2 y < 5 \end{cases}$ and the ordered pair is $(8, 3)$ .

Part b. Step 2. Substitute the values into the inequalities

Substitute $x = 8, y = 3$ into the first given inequality.

$3 \overset{?}{<} \frac{3}{2} (8) + 3 3 \overset{?}{<} 12 + 3 3 < 15 T r u e$

Substitute $x = 8, y = 3$ into the second given inequality.

$\frac{3}{4} (8) - 2 (3) \overset{?}{<} 5 6 - 6 \overset{?}{<} 5 0 < 5 T r u e$

Since both of the inequalities are satisfied, the given ordered pair is a solution to the system.

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91影视

In the following exercises, determine whether each ordered pair is a solution to the system.
$\{\begin{cases} y < \frac{3}{2} x + 3 \\ \frac{3}{4} x - 2 y < 5 \end{cases} a . (- 4, - 1) b . (8, 3)$

Short Answer

Step by step solution

Part a. Step 1. Given Information

Part a. Step 2. Substitute the values into the inequalities.

Part b. Step 1. Given Information

Part b. Step 2. Substitute the values into the inequalities

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91影视

In the following exercises, determine whether each ordered pair is a solution to the system. y<32x+334x-2y<5a.(-4,-1)b.(8,3)

Short Answer

Step by step solution

Part a. Step 1. Given Information

Part a. Step 2. Substitute the values into the inequalities.

Part b. Step 1. Given Information

Part b. Step 2. Substitute the values into the inequalities

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

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Probability and Statistics

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Study anywhere. Anytime. Across all devices.

In the following exercises, determine whether each ordered pair is a solution to the system.
$\{\begin{cases} y < \frac{3}{2} x + 3 \\ \frac{3}{4} x - 2 y < 5 \end{cases} a . (- 4, - 1) b . (8, 3)$