Algebra 1
Algebra 1
1st Edition
ISBN: 9780078884801
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Concept explainers

Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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Chapter 3, Problem 13QC
To determine

To solve the equation 3x+y=1 for y .

Expert Solution & Answer
Check Mark

Answer to Problem 13QC

  y=1−3x

Explanation of Solution

Given:

The equation, 3x+y=1 .

Concept Used:

  • To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
  • To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
  • To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
  • To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

  • Two numbers with similar sign always get added and the resulting number will carry the similar sign.
  • Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

  • The product/quotient of two similar sign numbers is always positive.
  • The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to solve the given equation 3x+y=1 for the variable, isolate the variable term y on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolateyon both side, first subtract both sides by3x and thensimplify further as shown below,

  3x+y=13x+y−3x=1−3xy=1−3x

Thus, the solution of the indicated variable is y=1−3x .

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Chapter 3, Problem 6QC
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Chapter 3, Problem 14QC

Chapter 3 Solutions

Algebra 1

Ch. 3.1 - Prob. 35PPSCh. 3.1 - Prob. 58PPSCh. 3.1 - Prob. 60HPCh. 3.1 - Prob. 68STPCh. 3.1 - Prob. 1ACYPCh. 3.1 - Prob. 1BCYPCh. 3.1 - Prob. 2CYPCh. 3.1 - Prob. 3CYPCh. 3.1 - Prob. 4ACYPCh. 3.1 - Prob. 4BCYP
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Prob. 15HPCh. 3.6 - Prob. 16HPCh. 3.6 - Prob. 17HPCh. 3.6 - Prob. 18HPCh. 3.6 - Prob. 1ACYPCh. 3.6 - Prob. 1BCYPCh. 3.6 - Prob. 1CCYPCh. 3.6 - Prob. 2ACYPCh. 3.6 - Prob. 2BCYPCh. 3.6 - Prob. 19STPCh. 3.6 - Prob. 20STPCh. 3.6 - Prob. 21STPCh. 3.6 - Prob. 22STPCh. 3.6 - Prob. 23SRCh. 3.6 - Prob. 24SRCh. 3.6 - Prob. 25SRCh. 3.6 - Prob. 26SRCh. 3.6 - Prob. 27SRCh. 3.6 - Prob. 28SRCh. 3.6 - Prob. 29SRCh. 3.6 - Prob. 30SCh. 3.6 - Prob. 31SCh. 3.6 - Prob. 32SCh. 3.6 - Prob. 33SCh. 3.6 - Prob. 34SCh. 3.6 - Prob. 35SCh. 3 - Prob. 1QCCh. 3 - Prob. 2QCCh. 3 - Prob. 3QCCh. 3 - Prob. 4QCCh. 3 - Prob. 5QCCh. 3 - Prob. 6QCCh. 3 - Prob. 13QCCh. 3 - Prob. 14QCCh. 3 - Prob. 15QCCh. 3 - Prob. 16QCCh. 3 - Prob. 17QCCh. 3 - Prob. 18QCCh. 3 - Prob. 19QCCh. 3 - Prob. 20QCCh. 3 - Prob. 21QCCh. 3 - Prob. 22QCCh. 3 - Prob. 23QCCh. 3 - Prob. 1MCQCh. 3 - Prob. 2MCQCh. 3 - Prob. 3MCQCh. 3 - Prob. 4MCQCh. 3 - Prob. 5MCQCh. 3 - Prob. 6MCQCh. 3 - Prob. 9MCQCh. 3 - Prob. 10MCQCh. 3 - Prob. 11MCQCh. 3 - Prob. 12MCQCh. 3 - 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