Question

Name each indicated property. If $3 x-7=y$, and $y=5 x+3$, then $3 x-7=5 x+3$

Name: Problem 14, Chapter 2: Intermediate Algebra for College Students
Uploaded: 2020-04-06T12:21:36-08:00
Duration: 51 s
Channel: Ankit Gupta
Description: Name each indicated property. If 3 x-7=y, and y=5 x+3, then 3 x-7=5 x+3

   Name each indicated property.
If $3 x-7=y$, and $y=5 x+3$, then $3 x-7=5 x+3$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 2, Problem 14

Instant Answer

Solved by Expert Ankit Gupta

04/06/2020

Step 1

First, we are given two equations: 1) $3x - 7 = y$ 2) $y = 5x + 3$ Show more…

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Name each indicated property. If $3 x-7=y$, and $y=5 x+3$, then $3 x-7=5 x+3$

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Key Concepts

Transitive Property of Equality

The transitive property of equality asserts that if one quantity equals a second quantity and the second equals a third, then the first equals the third. In this problem, because 3x - 7 equals y and y equals 5x + 3, it follows by the transitive property that 3x - 7 must equal 5x + 3.

Substitution Property of Equality

This property states that if two expressions are equal to the same value, one can replace one expression with the other in any equation. In the context of the problem, since y is defined by both 3x - 7 and 5x + 3, one of these expressions can be substituted for y in any equation involving y.

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