Q. 342 In the following exercises, solv... [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. 342 (page 679)

In the following exercises, solve the systems of equations by substitution.
$\{\begin{cases} 3 x - 2 y = 2 \\ y = \frac{1}{2} x + 3 \end{cases}$

Short Answer

Expert verified

The solution set is $(4, 5)$ .

Step by step solution

Step 1. Given Information

The given system of equations is $\{\begin{cases} 3 x - 2 y = 2 \\ y = \frac{1}{2} x + 3 \end{cases}$ .

Step 2. Find the value of x.

Substitute $y = \frac{1}{2} x + 3$ into the first given equation.

$\begin{array}{rcl} 3 x - 2 (\frac{1}{2} x + 3) & = & 2 \\ 3 x - x - 6 & = & 2 \\ 2 x & = & 8 \\ x & = & 4 \end{array}$

So, the value of $x$ is 4.

Step 3. Find the value of y.

Substitute $\begin{array}{rcl} x & = & 4 \end{array}$ into the second given equation.

$\begin{array}{rcl} y & = & \frac{1}{2} (4) + 3 \\ = & 2 + 3 \\ = & 5 \end{array}$

So, the solution set is $(4, 5)$ .

Step 4. Check the solution

Substitute $x = 4, y = 5$ into both the given equations and check if the equations are satisfied.

$3 (4) - 2 (5) \overset{?}{=} 2 12 - 10 \overset{?}{=} 2 2 = 2 5 \overset{?}{=} \frac{1}{2} (4) + 3 5 \overset{?}{=} 2 + 3 5 = 5$

As both the equations are satisfied, the solution is verified.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

In the following exercises, solve the systems of equations by substitution.
$\{\begin{cases} 3 x - 2 y = 2 \\ y = \frac{1}{2} x + 3 \end{cases}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find the value of x.

Step 3. Find the value of y.

Step 4. Check the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Logic and Functions

Probability and Statistics

Pure Maths

Calculus

Statistics

Study anywhere. Anytime. Across all devices.

91影视

In the following exercises, solve the systems of equations by substitution.3x-2y=2y=12x+3

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find the value of x.

Step 3. Find the value of y.

Step 4. Check the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Logic and Functions

Probability and Statistics

Pure Maths

Calculus

Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve the systems of equations by substitution.
$\{\begin{cases} 3 x - 2 y = 2 \\ y = \frac{1}{2} x + 3 \end{cases}$