To solve the system of equations:

1. **Equations**:
   - \(-4x + 4y = -20\)  (Equation 1)
   - \(y = -3x + 19\)    (Equation 2)

2. **Substitute Equation 2 into Equation 1**:
   Replace \(y\) in Equation 1 with \(-3x + 19\):
   \[
   -4x + 4(-3x + 19) = -20
   \]

3. **Simplify**:
   \[
   -4x - 12x + 76 = -20
   \]
   \[
   -16x + 76 = -20
   \]
   \[
   -16x = -20 - 76
   \]
   \[
   -16x = -96
   \]
   \[
   x = \frac{-96}{-16} = 6
   \]

4. **Find \(y\)**:
   Substitute \(x = 6\) back into Equation 2:
   \[
   y = -3(6) + 19
   \]
   \[
   y = -18 + 19 = 1
   \]

5. **Solution**:
   The solution to the system of equations is \(x = 6\) and \(y = 1\). Thus, the point of intersection is \((6, 1)\).

### Questions for Further Exploration:
1. How can we graph these equations to visualize their intersection?
2. What would happen to the solution if one of the equations was altered?
3. Can you provide an example of a system of equations that has no solution?
4. How would you solve these equations using the elimination method?
5. What real-world scenarios could be modeled by this system of equations?

### Tip:
When solving systems of equations, check your solution by substituting back into both original equations to ensure they hold true.

Discover how to solve the system of equations -4x + 4y = -20 and y = -3x + 19 through substitution. This step-by-step guide explains key algebraic concepts and methods. Perfect for students in Grades 8-10.

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