Is the ordered pair 

left parenthesis negative two sevenths comma negative three fifths right parenthesis−27,−35 

a solution of the equation 

77aplus+55bequals=11​? 

Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.

Yes because after substituting for a and​ b, it gives the result 

11equals=11.

B.

No because after substituting for a and​ b, it gives the result 

enter your response herenot equals≠11.

To determine whether the ordered pair \(\left(-\frac{2}{7}, -\frac{3}{5}\right)\) is a solution to the equation \(77a + 55b = 11\), we need to substitute the values of \(a = -\frac{2}{7}\) and \(b = -\frac{3}{5}\) into the equation and check if the equation holds true.

Substitute \(a = -\frac{2}{7}\) and \(b = -\frac{3}{5}\) into the equation:
\[
77\left(-\frac{2}{7}\right) + 55\left(-\frac{3}{5}\right) = 11
\]

First, calculate each term:
\[
77 \times \left(-\frac{2}{7}\right) = -22
\]
\[
55 \times \left(-\frac{3}{5}\right) = -33
\]

Now, add these results:
\[
-22 + (-33) = -55
\]

So, the left side of the equation is:
\[
-55 \neq 11
\]

Since \(-55\) does not equal \(11\), the equation does not hold true. Therefore, the correct choice is:

**B. No because after substituting for \(a\) and \(b\), it gives the result \(-55 \neq 11\).**

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:
1. How would you determine if another pair \((a, b)\) is a solution to the equation \(77a + 55b = 11\)?
2. Can the equation \(77a + 55b = 11\) be simplified further before substituting values?
3. What are the possible values of \(a\) and \(b\) that satisfy the equation \(77a + 55b = 11\)?
4. How can you solve the equation \(77a + 55b = 11\) for one variable in terms of the other?
5. What does the graph of the equation \(77a + 55b = 11\) look like?

**Tip:** When checking if a point satisfies an equation, always substitute the values carefully and simplify step by step to avoid errors.

Explore whether the ordered pair (-2/7, -3/5) satisfies the equation 77a + 55b = 11 through substitution and arithmetic operations. Understand the process of verifying solutions to linear equations in mathematics. Suitable for Grades 7-9.

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