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The given system of equations is:

1. \( y = -5x - 33 \)  (Equation 1)
2. \( 2y = 10x + 94 \)  (Equation 2)

We will solve this system using the substitution method. First, we'll express one variable in terms of the other, which has already been done for \( y \) in Equation 1.

### Step 1: Substitute \( y = -5x - 33 \) into Equation 2.

Substitute \( y \) into Equation 2:

\[
2(-5x - 33) = 10x + 94
\]

### Step 2: Simplify and solve for \( x \).

Expanding the left-hand side:

\[
-10x - 66 = 10x + 94
\]

Now, let's solve for \( x \):

\[
-10x - 66 = 10x + 94
\]
\[
-10x - 10x = 94 + 66
\]
\[
-20x = 160
\]
\[
x = \frac{160}{-20}
\]
\[
x = -8
\]

### Step 3: Substitute \( x = -8 \) back into Equation 1 to find \( y \).

Now substitute \( x = -8 \) into Equation 1:

\[
y = -5(-8) - 33
\]
\[
y = 40 - 33
\]
\[
y = 7
\]

### Final Solution:
The solution to the system of equations is:
\[
x = -8, \quad y = 7
\]

Would you like more details or have any questions?

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Here are 5 related questions to explore further:

1. How can we check if the solution \( x = -8 \) and \( y = 7 \) is correct?
2. Can this system be solved using the elimination method instead?
3. What happens if we substitute the values directly into Equation 2 without simplifying?
4. How do substitution and elimination methods differ in solving systems of equations?
5. What if both equations were linear in different forms? How would the method change?

**Tip:** Always verify your solution by plugging the values back into both original equations to ensure consistency.

Solve the system of equations using the substitution method: y = -5x - 33 and 2y = 10x + 94.

This guide walks through solving the system of linear equations: y = -5x - 33 and 2y = 10x + 94 using the substitution method, explaining each step from substitution to solving for both x and y.

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