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

6y+x=‒596y+x=‒59

x=‒2y+9x=‒2y+9


What is the value of yy in the solution to the system of equations?

A.8.58.5

B.‒17‒17

C.‒12.5‒12.5

D.4343


We are tasked with solving the system of equations:

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

### Step 1: Substitute the expression for \( x \) from the second equation into the first equation.

Since \( x = -2y + 9 \), substitute this into the first equation:

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

### Step 2: Simplify the equation.

Simplify the left-hand side:

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

This simplifies to:

\[
4y + 9 = -59
\]

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

Subtract 9 from both sides:

\[
4y = -59 - 9
\]

\[
4y = -68
\]

Now, divide by 4:

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

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

### Final Answer:

The value of \( y \) is \( \boxed{-17} \), which corresponds to option **B**.

---

Would you like a detailed explanation of any step or have any questions?

Here are 5 related questions to practice:

1. How would you solve a system of equations using substitution if both equations are already solved for \( x \)?
2. What is the process to solve a system of equations using elimination instead of substitution?
3. What is the graphical interpretation of solving a system of equations?
4. How can you determine if a system of equations has no solution or infinitely many solutions?
5. What are some applications of systems of equations in real-life problems?

**Tip:** Always check your solution by substituting the values of variables 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? A. 8.5 B. -17 C. -12.5 D. 43

Learn how to solve the system of equations 6y + x = -59 and x = -2y + 9 using the substitution method. This algebraic problem covers key concepts like solving for variables and simplifying equations. Ideal for students in Grades 8-10.

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