To solve the system of equations using the substitution method, we first isolate one variable in one equation and substitute it into the other equation.

Step 1: Write down the equations

1. $4x + 8y = 12$
2. $3x - 8y = 9$

Step 2: Solve one equation for one variable

From the first equation: $4x + 8y = 12 \implies 4x = 12 - 8y \implies x = \frac{12 - 8y}{4} \implies x = 3 - 2y$

Step 3: Substitute $x = 3 - 2y$ into the second equation

Substitute $x = 3 - 2y$ into $3x - 8y = 9$: $3(3 - 2y) - 8y = 9$ Simplify: $9 - 6y - 8y = 9 \implies 9 - 14y = 9$ $-14y = 0 \implies y = 0$

Step 4: Substitute $y = 0$ back into $x = 3 - 2y$

$x = 3 - 2(0) \implies x = 3$

Solution:

The solution to the system is: $x = 3, \, y = 0$

Final Answer:

$(x, y) = (3, 0)$

Would you like to see a graphical verification or additional details?

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Five related questions:

1. How is the substitution method different from the elimination method?
2. Can this system be solved graphically to verify the solution?
3. How do we interpret the solution of a linear system in terms of lines?
4. What are the steps to isolate a variable in more complex systems?
5. What if the equations represent parallel lines? What happens then?

Tip: Always simplify equations as much as possible before substituting to avoid unnecessary complexity.