https://file.aiquickdraw.com/mathbot/file/1727425495657cf4ny148.jpg

The system of equations shown in the image is:

\[
\begin{aligned}
    -4y + 20x &= -52 \\
    y &= -3x - 3
\end{aligned}
\]

To solve this system, we can use substitution since the second equation already expresses \( y \) in terms of \( x \).

### Step 1: Substitute \( y = -3x - 3 \) into the first equation:
\[
-4(-3x - 3) + 20x = -52
\]

### Step 2: Expand the equation:
\[
12x + 12 + 20x = -52
\]

### Step 3: Combine like terms:
\[
32x + 12 = -52
\]

### Step 4: Solve for \( x \):
\[
32x = -52 - 12
\]
\[
32x = -64
\]
\[
x = \frac{-64}{32} = -2
\]

### Step 5: Substitute \( x = -2 \) back into \( y = -3x - 3 \) to find \( y \):
\[
y = -3(-2) - 3
\]
\[
y = 6 - 3 = 3
\]

### Final solution:
\[
x = -2, \quad y = 3
\]

Would you like more details or explanations? Here are some related questions:

1. How do we solve systems of equations using substitution?
2. What is the elimination method for solving systems of equations?
3. Can all systems of equations be solved using substitution?
4. What are dependent and independent systems in terms of solutions?
5. How can we graphically interpret the solution to a system of equations?

**Tip:** When using substitution, always double-check the expression you substitute to ensure there are no sign errors.

Solve the system of equations: -4y + 20x = -52 and y = -3x - 3.

Learn how to solve the system of equations -4y + 20x = -52 and y = -3x - 3 using the substitution method. Detailed step-by-step explanation provided for Grades 8-10.

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