We are given the system of equations:

1. $x + y = -17$
2. $5x - 8y = 19$

We will solve this system using the substitution method.

Step 1: Solve one equation for one variable

From the first equation $x + y = -17$, solve for $x$: $x = -17 - y$

Step 2: Substitute the expression for $x$ into the second equation

Substitute $x = -17 - y$ into the second equation $5x - 8y = 19$: $5(-17 - y) - 8y = 19$

Step 3: Simplify and solve for $y$

Distribute the 5: $-85 - 5y - 8y = 19$ Combine like terms: $-85 - 13y = 19$ Add 85 to both sides: $-13y = 104$ Divide by -13: $y = -8$

Step 4: Substitute $y = -8$ back into the expression for $x$

Substitute $y = -8$ into $x = -17 - y$: $x = -17 - (-8) = -17 + 8 = -9$

Final Answer:

The solution to the system is: $(x, y) = (-9, -8)$

Would you like a detailed explanation of any step?

Here are 5 related questions to explore further:

1. How can we check the solution of the system by substitution?
2. Can the system be solved using the elimination method instead?
3. How does substitution compare to graphing for solving systems of equations?
4. What happens if the system of equations has no solution or infinitely many solutions?
5. How can systems of equations be applied to real-world problems?

Tip: Always verify your solution by plugging the values back into both original equations to ensure they satisfy both equations.