It looks like you've provided two systems of linear equations, but the formatting needs clarification. I'll interpret the equations as follows:

### System of Equations:
1. \( 2x - 4y = 6 \)
2. \( 3x + y = 2 \)

Let's solve this system of equations step by step.

### Step 1: Solve the second equation for \(y\)
From the second equation:
\[
3x + y = 2
\]
Solve for \(y\):
\[
y = 2 - 3x
\]

### Step 2: Substitute \(y\) into the first equation
Now, substitute \(y = 2 - 3x\) into the first equation:
\[
2x - 4(2 - 3x) = 6
\]

### Step 3: Simplify and solve for \(x\)
Distribute the \(-4\) on the left side:
\[
2x - 8 + 12x = 6
\]
Combine like terms:
\[
14x - 8 = 6
\]
Add 8 to both sides:
\[
14x = 14
\]
Divide by 14:
\[
x = 1
\]

### Step 4: Solve for \(y\)
Substitute \(x = 1\) back into the equation \(y = 2 - 3x\):
\[
y = 2 - 3(1) = 2 - 3 = -1
\]

### Final Answer:
The solution to the system of equations is:
\[
x = 1, \quad y = -1
\]

Would you like more details, or do you have any questions?

Here are 5 related questions you might find interesting:
1. How do you solve a system of linear equations using the substitution method?
2. What is the elimination method, and how does it work?
3. Can you graph the solution to the system of equations?
4. What happens if a system of equations has no solution or infinitely many solutions?
5. How would you solve a system of equations with three variables?

**Tip:** When solving systems of equations, it's useful to check your solution by plugging the values back into both original equations to ensure they are satisfied.

Learn how to solve the system of linear equations 2x - 4y = 6 and 3x + y = 2 step-by-step. This problem involves applying the substitution method to find the values of x and y. Suitable for high school students.

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