Chapter 5: Q.129 (page 626)

In the following exercises, solve the systems of equations by elimination.
$\{\begin{cases} 3 x - y = - 7 \\ 4 x + 2 y = - 6 \end{cases}$

Short Answer

Expert verified

The solution of the system is $(x, y) = (- 2, 1) .$

Step by step solution

Step 1. Given information

The given system is $\{\begin{cases} 3 x - y = - 7 \\ 4 x + 2 y = - 6 \end{cases}$

Step 2. solve for x

$\{\begin{cases} 3 x - y = - 7 \\ 4 x + 2 y = - 6 \end{cases} Given \{\begin{cases} 2 (3 x - y) = 2 (- 7) multiplyonbothsideswith2 \\ 4 x + 2 y = - 6 \end{cases} \{\begin{cases} 6 x - 2 y = - 14 \\ 4 x + 2 y = - 6 \end{cases} simplify$

Add both equations

$\begin{array}{l} 6 x - 2 y = - 14 \\ 4 x + 2 y = - 6 \end{array} 10 x = - 20 solvefor x x = \frac{- 20}{10} x = - 2$

Step 3. solve for y

$4 x + 2 y = - 6 secondequation 4 (- 2) + 2 y = - 6 use x = - 2 - 8 + 2 y = - 6 2 y = - 6 + 8 2 y = 2 y = \frac{2}{2} y = 1$

Step 4. Verify the solution

$\begin{array}{l} 3 x - y = - 7 \Rightarrow 3 (- 2) - 1 = - 7 \\ - 6 - 1 = - 7 \\ - 7 = - 7 true \\ 4 x + 2 y = - 6 \Rightarrow 4 (- 2) + 2 (1) = - 6 \\ - 8 + 2 = - 6 \\ - 6 = - 6 true \end{array}$

Both equations are true

Hence, the solution is $(x, y) = (- 2, 1)$ .

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In the following exercises, solve the systems of equations by elimination.
$\{\begin{cases} 3 x - y = - 7 \\ 4 x + 2 y = - 6 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. solve for x

Step 3. solve for y

Step 4. Verify the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Statistics

Probability and Statistics

Applied Mathematics

Geometry

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve the systems of equations by elimination.3x-y=-74x+2y=-6

Short Answer

Step by step solution

Step 1. Given information

Step 2. solve for x

Step 3. solve for y

Step 4. Verify the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Statistics

Probability and Statistics

Applied Mathematics

Geometry

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve the systems of equations by elimination.
$\{\begin{cases} 3 x - y = - 7 \\ 4 x + 2 y = - 6 \end{cases}$