Let's solve the system of equations using substitution.

The equations are:

1. $8x + 8y = -8$
2. $5x + y = 11$

Step 1: Solve one equation for one variable

From the second equation ($5x + y = 11$), isolate $y$: $y = 11 - 5x$

Step 2: Substitute into the first equation

Substitute $y = 11 - 5x$ into $8x + 8y = -8$: $8x + 8(11 - 5x) = -8$

Simplify: $8x + 88 - 40x = -8$

Combine like terms: $-32x + 88 = -8$

Solve for $x$: $-32x = -96 \quad \text{(subtract 88 from both sides)}$ $x = 3 \quad \text{(divide by -32)}$

Step 3: Solve for $y$

Substitute $x = 3$ into $y = 11 - 5x$: $y = 11 - 5(3)$ $y = 11 - 15$ $y = -4$

Final Solution:

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

Would you like further details or a verification? Here are five related questions:

1. How can we verify this solution by substituting back into both equations?
2. How does substitution compare to other methods like elimination for solving systems?
3. Can you graph the equations to confirm the intersection point is $(3, -4)$?
4. How would the solution change if one of the equations was altered slightly?
5. Are there cases where substitution might fail or be less efficient?

Tip: Always double-check solutions by substituting them back into the original equations!