Is the ordered pair left parenthesis negative six sevenths comma negative five eighths right parenthesis
 
a solution of the equation 7
aplus8bequals1​? 
Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

We need to check whether the ordered pair \((- \frac{6}{7}, - \frac{5}{8})\) is a solution to the equation \(7a + 8b = 1\).

In this context, \(a = - \frac{6}{7}\) and \(b = - \frac{5}{8}\). Substitute these values into the equation:

\[
7a + 8b = 7 \left( - \frac{6}{7} \right) + 8 \left( - \frac{5}{8} \right)
\]

Let's simplify:

\[
7 \left( - \frac{6}{7} \right) = -6
\]
\[
8 \left( - \frac{5}{8} \right) = -5
\]

Now add these values:

\[
-6 + (-5) = -11
\]

The result is \(-11\), but the equation we are checking against is \(7a + 8b = 1\), not \(-11\). Therefore, \((- \frac{6}{7}, - \frac{5}{8})\) is **not** a solution to the equation.

### Final answer:
The correct choice is that \((- \frac{6}{7}, - \frac{5}{8})\) **is not** a solution to the equation \(7a + 8b = 1\).

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Would you like further details or explanations? Here are some additional related questions for practice:

1. Solve \(7a + 8b = 1\) for \(a\) given a value for \(b\).
2. Check if the ordered pair \(\left( \frac{1}{2}, \frac{1}{3} \right)\) is a solution to \(7a + 8b = 1\).
3. Determine the solution set of \(7a + 8b = 1\).
4. What is the significance of the ordered pair in the context of solving systems of linear equations?
5. How do you interpret the slope of the line represented by \(7a + 8b = 1\)?

**Tip:** When checking if an ordered pair is a solution, always substitute both values carefully and simplify step by step to avoid errors.

Is the ordered pair (-6/7, -5/8) a solution of the equation 7a + 8b = 1?

Explore whether the ordered pair (-6/7, -5/8) solves the equation 7a + 8b = 1 by substituting and simplifying. This problem covers core algebraic concepts such as solving linear equations and substitution, ideal for students in Grades 6-8.

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