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 for \( y \), we can substitute the expression for \( x \) from the second equation 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:

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

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

Would you like more details on solving systems of equations, or do you have any other questions?

### Related Questions:
1. What is the value of \( x \) in this system?
2. How can substitution be applied to solve systems of equations?
3. What methods other than substitution can solve a system of equations?
4. How does elimination compare to substitution when solving systems of equations?
5. Can you graphically interpret the solution to this system?

### Tip:
Always check the solution by substituting both values of \( x \) and \( y \) back into the original equations to verify correctness.

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. This step-by-step solution explores algebraic concepts, including solving systems of equations and applying substitution. Perfect for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation