To solve the equation $4x + 2y = 4$ for $x$ and $y$, we have a linear equation in two variables. Typically, a single linear equation doesn't have a unique solution for both variables unless there's additional information (like another equation to form a system). However, we can express one variable in terms of the other.

Let's solve for $y$ in terms of $x$:

Step 1: Simplify the equation

$4x + 2y = 4$ Divide through by 2 to simplify: $2x + y = 2$

Step 2: Solve for $y$

Now, solve for $y$: $y = 2 - 2x$

Thus, $y$ is expressed as a function of $x$: $y = 2 - 2x$

Interpretation:

The equation represents a line, and for every value of $x$, there is a corresponding value of $y$. There are infinitely many solutions that satisfy this equation, which all lie on the line.

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Would you like more details, or have any questions about this process?

Related questions:

1. What would the graph of this equation look like?
2. How do you solve a system of two linear equations?
3. What is the slope and y-intercept of this line?
4. How would the solution change if there was another equation involved?
5. How do you solve this using matrix methods?

Tip:

For equations with two variables, graphing the equation can help visualize the set of possible solutions!