solve the following equation for x and y : 4x + 2y = 4

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!

Learn how to solve the linear equation 4x + 2y = 4 by expressing one variable in terms of the other. This problem explores key algebraic concepts such as solving linear equations and graphing their solutions. Suitable for students in Grades 7-10.

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