The image contains a system of linear equations:

1. $-x - 2y = 16$
2. $y = 4x + 19$

Let's solve this system step-by-step using substitution.

Step 1: Substitution

Since $y$ is already expressed as $y = 4x + 19$, substitute this into the first equation.

$-x - 2(4x + 19) = 16$

Step 2: Simplify

Distribute $-2$ to the terms in the parentheses:

$-x - 8x - 38 = 16$

Combine like terms:

$-9x - 38 = 16$

Add 38 to both sides:

$-9x = 54$

Divide by $-9$:

$x = -6$

Step 3: Solve for $y$

Substitute $x = -6$ into $y = 4x + 19$:

$y = 4(-6) + 19$

$y = -24 + 19$

$y = -5$

Final Solution:

$x = -6, \, y = -5$

Would you like me to verify the solution or provide further details?

Related Questions:

1. How do you graphically represent a system of equations like this one?
2. What is the significance of the substitution method for solving systems of equations?
3. Can elimination be used to solve this problem, and how would it differ from substitution?
4. What happens if the system of equations has no solution or infinitely many solutions?
5. How can you use matrices to solve systems of linear equations?

Tip:

Always double-check your solutions by substituting them back into the original equations to ensure accuracy!