You have two equations:

1. $y = 2x$
2. $x = -y + 6$

We can solve this system of equations by substitution or elimination. Let's use substitution.

Step 1: Substitute the expression for $y$ from the first equation into the second equation.

From the first equation, we know that $y = 2x$. Substitute this into the second equation:

$x = -(2x) + 6$

Step 2: Simplify and solve for $x$.

$x = -2x + 6$

Add $2x$ to both sides to isolate terms with $x$:

$3x = 6$

Now, divide by 3 to solve for $x$:

$x = 2$

Step 3: Substitute $x = 2$ back into the first equation to solve for $y$.

Using $y = 2x$ and substituting $x = 2$:

$y = 2(2) = 4$

Solution:

The solution to the system of equations is: $x = 2, \quad y = 4$

Do you want to see the solution process with a different method or have any other questions?

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Here are 5 related questions for you to explore:

1. What is the method of elimination, and how can it be used to solve this system of equations?
2. How can we solve a system of equations when both equations are in terms of $y$?
3. What happens if you have a system of equations with no solution or infinitely many solutions?
4. How would you graph these two equations to find their intersection point?
5. Can you solve systems of nonlinear equations (like quadratic or cubic equations) in a similar way?

Tip: Always check your solution by substituting the values of $x$ and $y$ back into both original equations to ensure they satisfy both.