Question

The sum of two numbers is $2 .$ If one number is subtracted from the other, their difference is $8 .$ Find the numbers. Three times a first number decreased by a second number is 1. The first number increased by twice the second number is 12. Find the numbers.

Name: Problem 45, Chapter 5: College Algebra
Uploaded: 2022-10-12T18:07:39-08:00
Duration: 1 min 58 s
Channel: Nicole Hoffman
Description: The sum of two numbers is 2 . If one number is subtracted from the other, their difference is 8 . Find the numbers. Three times a first number decreased by a second number is 1. The first number increased by twice the second number is 12. Find the numbers.

   The sum of two numbers is $2 .$ If one number is subtracted from the other, their difference is $8 .$ Find the numbers.
Three times a first number decreased by a second number
is 1. The first number increased by twice the second number
is 12. Find the numbers.

College Algebra

Robert Blitzer 7th Edition

Chapter 5, Problem 45

Instant Answer

Solved by Expert Nicole Hoffman

10/12/2022

Step 1

Let's denote the first number as $x$ and the second number as $y$. The problem gives us two equations: \begin{align*} 3x - y &= 1, \\ x + 2y &= 12. \end{align*} Show more…

Show all steps

Thanks for your feedback!

The sum of two numbers is $2 .$ If one number is subtracted from the other, their difference is $8 .$ Find the numbers. Three times a first number decreased by a second number is 1. The first number increased by twice the second number is 12. Find the numbers.

Play audio

Feedback

Nicole Hoffman and 81 other subject Algebra educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Systems of Linear Equations

A system of linear equations consists of two or more linear equations involving the same set of variables. Solving the system means finding values for the variables that satisfy all equations simultaneously, a fundamental concept in algebra used to solve many real-world problems.

Translation of Verbal Descriptions to Equations

This concept involves converting word problems into algebraic equations. It requires interpreting the relationships and conditions described in the problem text and formulating them mathematically, which lays the groundwork for solving the system as a whole.

Algebraic Methods for Solving Systems

Once a system of equations has been established, algebraic methods such as substitution or elimination are employed to solve for the unknown variables. These techniques simplify the system step-by-step until the values of the variables are determined.

Please give Ace some feedback