Given `[{:(,3,-8),(,9,4):}] [{:(,x),(,y):}]=[{:(,-2),(,8):}]`, find x and y.

Answer

To solve the equation given by the matrices, we need to find the values of \( x \) and \( y \) from the equation:

\[ \begin{pmatrix} 3 & -8 \\ 9 & 4 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} -2 \\ 8 \end{pmatrix} \]

### Step 1: Set up the equations
From the matrix multiplication, we can derive two equations:

1. \( 3x - 8y = -2 \) (Equation 1)
2. \( 9x + 4y = 8 \) (Equation 2)

### Step 2: Solve for one variable
Let's solve Equation 1 for \( x \):

\[ 3x = -2 + 8y \]
\[ x = \frac{-2 + 8y}{3} \]

### Step 3: Substitute into the second equation
Now, substitute \( x \) in Equation 2:

\[ 9\left(\frac{-2 + 8y}{3}\right) + 4y = 8 \]

### Step 4: Clear the fraction
Multiply through by 3 to eliminate the fraction:

\[ 9(-2 + 8y) + 12y = 24 \]
\[ -18 + 72y + 12y = 24 \]
\[ 84y - 18 = 24 \]

### Step 5: Solve for \( y \)
Add 18 to both sides:

\[ 84y = 24 + 18 \]
\[ 84y = 42 \]
\[ y = \frac{42}{84} = \frac{1}{2} \]

### Step 6: Substitute \( y \) back to find \( x \)
Now substitute \( y = \frac{1}{2} \) back into Equation 1:

\[ 3x - 8\left(\frac{1}{2}\right) = -2 \]
\[ 3x - 4 = -2 \]
\[ 3x = -2 + 4 \]
\[ 3x = 2 \]
\[ x = \frac{2}{3} \]

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

\[ x = \frac{2}{3}, \quad y = \frac{1}{2} \]