Use substitution to determine whether the given ordered pairs are solutions of the given equation.
left parenthesis five thirds comma one fourth right parenthesis
​, left parenthesis 1 comma five halves right parenthesis
​; 6xminus4yequalsnegative 4
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Part 1
Is left parenthesis five thirds comma one fourth right parenthesis
a​ solution?

To determine whether the given ordered pair \(\left(\frac{5}{3}, \frac{1}{4}\right)\) is a solution of the equation \(6x - 4y = -4\), we can substitute \(x = \frac{5}{3}\) and \(y = \frac{1}{4}\) into the equation and see if the equation holds true.

Given equation:
\[
6x - 4y = -4
\]

Substitute \(x = \frac{5}{3}\) and \(y = \frac{1}{4}\) into the equation:

\[
6\left(\frac{5}{3}\right) - 4\left(\frac{1}{4}\right) = -4
\]

Now, calculate each term:

1. \(6 \times \frac{5}{3} = 2 \times 5 = 10\)
2. \(4 \times \frac{1}{4} = 1\)

So, the equation becomes:

\[
10 - 1 = 9
\]

Since \(9 \neq -4\), the equation does not hold true.

Therefore, the ordered pair \(\left(\frac{5}{3}, \frac{1}{4}\right)\) **is not** a solution to the equation \(6x - 4y = -4\).

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you determine if an ordered pair is a solution to a linear equation?
2. Can you graphically interpret the result of this problem?
3. What is the geometric meaning of a solution to a linear equation?
4. How would you solve the equation \(6x - 4y = -4\) for \(y\)?
5. What would happen if you substituted another pair into the equation?

**Tip:** Always check your calculations carefully when substituting values to avoid simple errors.

Learn how to determine if an ordered pair is a solution to a linear equation using the substitution method with a detailed step-by-step solution. This problem involves the equation 6x - 4y = -4 and checks if the ordered pairs (5/3, 1/4) and (1, 5/2) are solutions. Suitable for students in Grades 7-9.

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