We are given the system of equations:

1. \( 6y + x = -59 \)
2. \( x = -2y + 9 \)

We can substitute the expression for \( x \) from the second equation into the first equation. 

Substitute \( x = -2y + 9 \) into \( 6y + x = -59 \):

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

Simplify the equation:

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

\[
4y + 9 = -59
\]

Now, subtract 9 from both sides:

\[
4y = -59 - 9
\]

\[
4y = -68
\]

Now, divide both sides by 4:

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

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

Would you like details on this solution or have any questions?

Here are 5 related questions:
1. What is the value of \( x \) using \( y = -17 \)?
2. Can you graph these two equations and interpret the solution?
3. How would the system change if we altered one of the constants in the equations?
4. What method can be used to solve a system of equations graphically?
5. How can you verify the solution by substitution?

**Tip**: When solving systems of equations, substitution is often easier when one of the equations is already solved for a variable.

6y + x = -59, x = -2y + 9, what is the y value?

Learn how to solve the system of linear equations 6y + x = -59 and x = -2y + 9 using the substitution method. This detailed step-by-step guide is perfect for students in Grades 8-10 studying algebraic systems of equations.

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