We are asked to solve the following system of equations: $x + 2y = 2$ $3x + 6y = 8$ If the system has no solution, we should enter "NO SOLUTION".

1. Problem Description

We are asked to solve the following system of equations:

$x + 2y = 2$

$3x + 6y = 8$

If the system has no solution, we should enter "NO SOLUTION".

2. Solution Steps

We can use the elimination method.

Multiply the first equation by -3:

$-3(x + 2y) = -3(2)$

$-3x - 6y = -6$

Now add this equation to the second equation:

$(-3x - 6y) + (3x + 6y) = -6 + 8$

$0 = 2$

This is a contradiction. Since we arrived at a contradiction, the system has no solution.

3. Final Answer

NO SOLUTION