To solve the system of equations using substitution:

The given system is:

1. $x = -y$
2. $8x + 3y = 40$

Step 1: Substitute $x = -y$ into the second equation.

Substitute $-y$ for $x$ in the second equation:

$8(-y) + 3y = 40$

$-8y + 3y = 40$

$-5y = 40$

Step 2: Solve for $y$.

Divide both sides by $-5$:

$y = -8$

Step 3: Substitute $y = -8$ back into $x = -y$.

Substitute $-8$ for $y$:

$x = -(-8)$

$x = 8$

Final Solution:

$x = 8, \, y = -8$

If you have further questions or would like a detailed explanation of any step, let me know!

Here are 5 follow-up questions to deepen your understanding:

1. How can we check if the solution satisfies both equations?
2. What are the advantages of substitution over other methods like elimination?
3. Could this system have no solutions or infinitely many solutions? Why or why not?
4. What would the graph of this system of equations look like?
5. How does substitution work when equations are in a more complex form?

Tip: Always substitute your solution back into the original equations to verify its correctness.