Let's solve the system of equations using the elimination method:

$-8x + 8y = 8$ $3x - 4y = -12$

Step 1: Multiply the equations to align coefficients

We want to eliminate one variable. Let's eliminate y by making the coefficients of $y$ equal. The least common multiple of 8 and 4 is 8, so we multiply the second equation by 2:

$-8x + 8y = 8$ $(3x - 4y) \times 2 = ( -12) \times 2$

$6x - 8y = -24$

Step 2: Add the equations

$(-8x + 8y) + (6x - 8y) = 8 + (-24)$

$-2x = -16$

Step 3: Solve for $x$

$x = \frac{-16}{-2} = 8$

Step 4: Substitute $x = 8$ into one of the original equations

Using $-8x + 8y = 8$:

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

$-64 + 8y = 8$

$8y = 72$

$y = 9$

Final Answer:

$(x, y) = (8, 9)$

Would you like a more detailed breakdown of any step?

Here are 5 related questions you might find interesting:

1. How does the elimination method compare to the substitution method?
2. What happens if both variables get eliminated and you get a true statement like $0 = 0$?
3. How do you solve a system of three equations using elimination?
4. Can elimination be used if the equations involve fractions?
5. What is the graphical interpretation of solving a system using elimination?

Tip: Always check your solution by plugging $x$ and $y$ back into the original equations!