Find the values of X and Y
`[{:(x+y),(" "3x""):}]=[{:(-2),(6):}].`

Explanation

To solve the problem, we need to find the values of \( X \) and \( Y \) from the given matrix equation:

\[ \begin{pmatrix} x + y \\ 3x \end{pmatrix} = \begin{pmatrix} -2 \\ 6 \end{pmatrix} \]

### Step 1: Equate the corresponding elements of the matrices

From the matrix equation, we can set up two equations by equating the corresponding elements:

1. \( x + y = -2 \) (Equation 1)
2. \( 3x = 6 \) (Equation 2)

### Step 2: Solve Equation 2 for \( x \)

From Equation 2, we can solve for \( x \):

\[ 3x = 6 \]

Dividing both sides by 3:

\[ x = \frac{6}{3} = 2 \]

### Step 3: Substitute \( x \) into Equation 1 to find \( y \)

Now that we have \( x = 2 \), we can substitute this value into Equation 1:

\[ x + y = -2 \]

Substituting \( x = 2 \):

\[ 2 + y = -2 \]

### Step 4: Solve for \( y \)

To solve for \( y \), we subtract 2 from both sides:

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

### Final Values

Thus, the values of \( x \) and \( y \) are:

\[ x = 2, \quad y = -4 \]

### Summary

The final answer is:
- \( x = 2 \)
- \( y = -4 \)