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We are given a system of equations:

\[
6y + x = -59 \quad \text{(1)}
\]
\[
x = -2y + 9 \quad \text{(2)}
\]

We can solve this system by substitution. First, from equation (2), we know that:

\[
x = -2y + 9
\]

We substitute this expression for \(x\) into equation (1):

\[
6y + (-2y + 9) = -59
\]

Simplifying:

\[
6y - 2y + 9 = -59
\]
\[
4y + 9 = -59
\]

Now, subtract 9 from both sides:

\[
4y = -59 - 9
\]
\[
4y = -68
\]

Finally, divide by 4:

\[
y = \frac{-68}{4} = -17
\]

Thus, the value of \(y\) is \(-17\).

The correct answer is **D. \(-17\)**.

Would you like any more details or further explanation?

Here are 5 follow-up questions to deepen your understanding:
1. How would you solve the system using the elimination method?
2. What would happen if we swapped the two equations in the substitution method?
3. Can you solve this system graphically? What would the intersection represent?
4. If the second equation were modified, how would that affect the solution?
5. How can you verify the solution by plugging back values into both equations?

**Tip**: Always double-check your final solution by substituting it back into the original equations to ensure accuracy!

Mrs. Flores asked her students to solve the following system of equations: 6y + x = -59 and x = -2y + 9. What is the value of y in the solution to the system of equations?

Learn how to solve the system of equations 6y + x = -59 and x = -2y + 9 using the substitution method. This problem covers key algebraic concepts and step-by-step calculations suitable for students in Grades 8-10.

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