Which of the given values of x and y make the following pair of matrices equal `[3x+7 5y+1 2-3x],[0y-2 8 4]` (a) `x=(-1)/3, y=7` (b) Not possible to find (c) `y=7, x=(-2)/3` (d) `x=(-1)/3, y=(-2)/3`

Explanation

To determine which of the given values of \( x \) and \( y \) make the following pair of matrices equal:

\[ \begin{bmatrix} 3x + 7 & 5y + 1 & 2 - 3x \\ \end{bmatrix} = \begin{bmatrix} 0y - 2 & 8 & 4 \\ \end{bmatrix} \]

We need to equate corresponding elements of the matrices.

### Step 1: Set up the equations
From the matrices, we can set up the following equations based on the corresponding elements:

1. \( 3x + 7 = -2 \)
2. \( 5y + 1 = 8 \)
3. \( 2 - 3x = 4 \)

### Step 2: Solve the first equation
Starting with the first equation:

\[ 3x + 7 = -2 \]

Subtract 7 from both sides:

\[ 3x = -2 - 7 \]
\[ 3x = -9 \]

Now divide by 3:

\[ x = -3 \]

### Step 3: Solve the second equation
Now, let's solve the second equation:

\[ 5y + 1 = 8 \]

Subtract 1 from both sides:

\[ 5y = 8 - 1 \]
\[ 5y = 7 \]

Now divide by 5:

\[ y = \frac{7}{5} \]

### Step 4: Solve the third equation
Now, let's solve the third equation:

\[ 2 - 3x = 4 \]

Subtract 2 from both sides:

\[ -3x = 4 - 2 \]
\[ -3x = 2 \]

Now divide by -3:

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

### Step 5: Check for consistency
We have found:

- From the first equation: \( x = -3 \)
- From the second equation: \( y = \frac{7}{5} \)
- From the third equation: \( x = -\frac{2}{3} \)

Since the values of \( x \) obtained from the first and third equations are different, it is not possible to find consistent values for \( x \) and \( y \) that satisfy all equations simultaneously.

### Conclusion
Thus, the answer is option (b): Not possible to find.

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