To solve the system of equations:

1. Equation 1: $4x + 9y = -19$
2. Equation 2: $-4x - 7y = 13$

We can use the elimination method. First, let's add both equations to eliminate $x$:

$(4x + 9y) + (-4x - 7y) = -19 + 13$

This simplifies to:

$(4x - 4x) + (9y - 7y) = -6$

$2y = -6$

Now, divide both sides by 2:

$y = -3$

Next, substitute $y = -3$ back into Equation 1 to find $x$:

$4x + 9(-3) = -19$

This simplifies to:

$4x - 27 = -19$

Adding 27 to both sides gives:

$4x = 8$

Now, divide by 4:

$x = 2$

Thus, the solution to the system of equations is:

$x = 2, \quad y = -3$

Summary of Solution:

• $x = 2$
• $y = -3$

Would you like any further details or explanations? Here are some related questions you might consider:

1. How would the solution change if one of the equations were modified?
2. Can you demonstrate the substitution method for this system?
3. What does the solution represent graphically?
4. How can we verify the solution using both equations?
5. What are some real-world applications of solving systems of equations?

Tip: Always check your solution by substituting the values back into the original equations!