-x-4y=2 and x+4y=-2 what is the value of x and y

We are given the system of linear equations:

\[
-x - 4y = 2 \quad \text{(1)}
\]
\[
x + 4y = -2 \quad \text{(2)}
\]

### Step 1: Add the two equations.
By adding equations (1) and (2), we eliminate \(y\):

\[
(-x - 4y) + (x + 4y) = 2 + (-2)
\]
\[
0 = 0
\]

This result indicates that the two equations are dependent, meaning they represent the same line. Therefore, there are infinitely many solutions, and \(x\) and \(y\) are dependent on each other.

### Step 2: Express one variable in terms of the other.
From equation (2), solve for \(x\):

\[
x + 4y = -2
\]
\[
x = -2 - 4y
\]

Thus, \(x\) is expressed in terms of \(y\). For any value of \(y\), we can calculate \(x\) using this equation.

### Final Answer:
The system has infinitely many solutions. The solution set is:
\[
x = -2 - 4y \quad \text{for any value of } y.
\]

Let me know if you would like a specific example or further clarification!

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Here are 5 related questions:
1. How do you solve systems of linear equations using substitution?
2. What are the different methods to solve a system of equations?
3. How do you interpret the result when the system of equations has infinitely many solutions?
4. What is the graphical representation of a system of dependent equations?
5. Can systems of equations have no solution? How is that identified?

**Tip:** When two equations lead to a result like \(0 = 0\), this usually means the lines are the same, leading to infinite solutions.

x - 4y = 2 and x + 4y = -2 what is the value of x and y?

Learn how to solve the system of linear equations x - 4y = 2 and x + 4y = -2, which leads to infinitely many solutions. This problem demonstrates the concept of dependent equations, where the variables are related to each other. Suitable for students in Grades 9-10.

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