We are given two equations to solve by substitution:

1. $y = -5x - 19$
2. $y = 2x + 2$

Steps for Substitution:

1. Since both equations are already solved for $y$, we can set the two expressions for $y$ equal to each other: $-5x - 19 = 2x + 2$

2. Solve for $x$:

   • Add $5x$ to both sides: $-19 = 7x + 2$

   • Subtract 2 from both sides: $-21 = 7x$

   • Divide by 7: $x = -3$

3. Substitute $x = -3$ back into one of the original equations to find $y$. Let's use the second equation $y = 2x + 2$: $y = 2(-3) + 2 = -6 + 2 = -4$

Thus, the solution is $x = -3$ and $y = -4$.

Final Answer:

$(x, y) = (-3, -4)$

Would you like any further details or clarification?

Here are some related questions to consider:

1. How would you solve the system using elimination instead of substitution?
2. How can you graphically interpret the solution to these equations?
3. What if the slopes were equal? What type of solution would we expect?
4. How do you verify the solution by substituting it back into both equations?
5. What is the significance of the point $(-3, -4)$ on the graph?

Tip: When solving systems of equations, always check your solution by substituting it back into both original equations to verify its correctness.