Mrs. Flores asked her students to solve the following system of equations.

6y+x=‒59
x=‒2y+9

What is the value of y
in the solution to the system of equations?
A.8.5

B.‒17

C.43

D.‒12.5

We are given the system of equations:

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

To solve this system, we can use substitution. Since the second equation gives us an expression for \(x\), we can substitute that into the first equation.

### Step 1: Substitute \( x = -2y + 9 \) into the first equation

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

### Step 2: Simplify the equation

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

\[
4y + 9 = -59
\]

### Step 3: Solve for \( y \)

Subtract 9 from both sides:

\[
4y = -59 - 9
\]

\[
4y = -68
\]

Now, divide both sides by 4:

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

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

### Answer:
The correct answer is **B. -17**.

Would you like more details on this solution? 

Here are 5 related questions to expand on this topic:

1. How do you solve a system of equations using substitution?
2. What is the graphical interpretation of solving a system of equations?
3. Can systems of equations have no solution or infinite solutions?
4. How do you check if your solution to a system of equations is correct?
5. What is the difference between substitution and elimination methods?

**Tip:** When solving systems of equations, always ensure that the substitution or elimination simplifies one variable before proceeding to solve for the second variable.

Mrs. Flores asked her students to solve the following system of equations.

6y + x = ‒59
x = ‒2y + 9

What is the value of y in the solution to the system of equations?
A. 8.5
B. ‒17
C. 43
D. ‒12.5

Learn how to solve the system of equations 6y + x = ‒59 and x = ‒2y + 9 using the substitution method. Follow a detailed step-by-step solution to find the correct value of y. This algebra problem is suitable for students in Grades 8-10.

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