Find the values of 'x' and 'y' when :
`[(x+2y,3y),(4x,2)]=[(0,-3),(8,2)]`

Answer

To find the values of 'x' and 'y' from the equation of matrices, we start with the given matrices:

\[ \begin{pmatrix} x + 2y & 3y \\ 4x & 2 \end{pmatrix} = \begin{pmatrix} 0 & -3 \\ 8 & 2 \end{pmatrix} \]

Since the two matrices are equal, we can equate the corresponding elements.

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

1. From the first element (top left):
\[ x + 2y = 0 \quad \text{(1)} \]

2. From the second element (top right):
\[ 3y = -3 \quad \text{(2)} \]

3. From the third element (bottom left):
\[ 4x = 8 \quad \text{(3)} \]

4. From the fourth element (bottom right):
\[ 2 = 2 \quad \text{(This is always true and does not provide new information)} \]

### Step 2: Solve the equations

**From equation (2):**
\[ 3y = -3 \]
Dividing both sides by 3:
\[ y = -1 \]

**From equation (3):**
\[ 4x = 8 \]
Dividing both sides by 4:
\[ x = 2 \]

### Step 3: Verify with equation (1)

Now we can substitute the values of \(x\) and \(y\) back into equation (1) to verify:
\[ x + 2y = 0 \]
Substituting \(x = 2\) and \(y = -1\):
\[ 2 + 2(-1) = 2 - 2 = 0 \]
This confirms that our values are correct.

### Final Values
Thus, the values of \(x\) and \(y\) are:
\[ x = 2, \quad y = -1 \]

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