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Chapter 2: Problem 35

Determine whether each ordered pair is a solution of the given equation. Remember to use alphabetical order for substitution. \(\left(\frac{2}{3}, 0\right) ; 6 x+8 y=4\)

Short Answer

Expert verified
Yes, the ordered pair \( \left( \frac{2}{3}, 0 \right) \) is a solution of the equation \( 6x + 8y = 4 \).

Step by step solution

01

Understand the Given Equation

The given equation is: \[6x + 8y = 4\] We need to check if the ordered pair \( \left(\frac{2}{3}, 0\right) \) is a solution to this equation.
02

Identify the Values of x and y

From the ordered pair \( \left( \frac{2}{3}, 0 \right) \), we have: \[ x = \frac{2}{3} \text{ and } y = 0 \]
03

Substitute the Values into the Equation

Substitute \( x = \frac{2}{3} \) and \( y = 0 \) into the equation \( 6x + 8y = 4 \) to verify if it holds true: \[ 6 \left( \frac{2}{3} \right) + 8(0) \]
04

Simplify the Expression

Simplify the left-hand side of the equation: \[ 6 \left( \frac{2}{3} \right) + 8(0) = 4 \] \[ 4 + 0 = 4 \] \[ 4 = 4 \]
05

Determine the Result

Since the left-hand side \( 4 \) equals the right-hand side \( 4 \), the equation \( 6x + 8y = 4 \) holds true for the ordered pair \( \left( \frac{2}{3}, 0 \right) \). Therefore, the ordered pair is a solution to the equation.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Ordered Pairs
In mathematics, an **ordered pair** is a pair of elements used to locate points on a coordinate plane. An ordered pair is written in the

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