Let's solve the given equation:

$2x + 4y = 4x + 8y$

Step 1: Move like terms to one side

Rearrange the terms to bring all $x$ and $y$ terms to one side:

$2x + 4y - 4x - 8y = 0$

Step 2: Combine like terms

$(2x - 4x) + (4y - 8y) = 0$

$-2x - 4y = 0$

Step 3: Factor out $-2$

$-2(x + 2y) = 0$

Step 4: Solve for $x + 2y$

$x + 2y = 0$

Conclusion:

The equation simplifies to $x + 2y = 0$, which represents a linear relationship between $x$ and $y$. This equation does not give a single numerical solution but rather an infinite number of solutions depending on the value of $y$.

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Related Questions:

1. How do you graph the equation $x + 2y = 0$?
2. What are some specific solutions to $x + 2y = 0$?
3. How do you express $x$ in terms of $y$ from $x + 2y = 0$?
4. Can this equation be rewritten in slope-intercept form?
5. How does this equation compare to $2x + 4y = 8$?

Math Tip:

When solving equations, always check if you can factor or simplify terms to make solving easier.