Chapter 6: Q20. (page 393)

Use an augmented matrix to solve each system of equations.
$x + y = 15 x - y = 9$

Short Answer

Expert verified

The solution of the given system of equations is $(12, 3)$ .

Step by step solution

Step 1. Write the augmented matrix for the given system of equations.

The given system of equations is:

$x + y = 15 x - y = 9$

Place the coefficients of the equations and the constant terms into the matrix to form the augmented matrix for the given system of equations.

$[\begin{matrix} 1 & 1 & 15 \\ 1 & - 1 & 9 \end{matrix}]$

Step 2. Solve the given system of equations.

The augmented matrix is:

$[\begin{matrix} 1 & 1 & 15 \\ 1 & - 1 & 9 \end{matrix}]$

Apply $R_{2} \to R_{2} - R_{1}$ ,

$[\begin{matrix} 1 & 1 & 15 \\ 0 & - 2 & - 6 \end{matrix}]$

Apply $R_{2} \to \frac{- 1}{2} R_{2}$ ,

$[\begin{matrix} 1 & 1 & 15 \\ 0 & 1 & 3 \end{matrix}]$

Apply $R_{1} \to R_{1} - R_{2}$ ,

$[\begin{matrix} 1 & 0 & 12 \\ 0 & 1 & 3 \end{matrix}]$

Therefore, the solution of the given system of equations is $(12, 3)$ .

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.

Use an augmented matrix to solve each system of equations.
$x + y = 15 x - y = 9$

Short Answer

Step by step solution

Step 1. Write the augmented matrix for the given system of equations.

Step 2. Solve the given system of equations.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Logic and Functions

Pure Maths

Decision Maths

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Use an augmented matrix to solve each system of equations.x+y=15x−y=9

Short Answer

Step by step solution

Step 1. Write the augmented matrix for the given system of equations.

Step 2. Solve the given system of equations.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Logic and Functions

Pure Maths

Decision Maths

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Use an augmented matrix to solve each system of equations.
$x + y = 15 x - y = 9$