Which of the given values of x and y make the following pair of matrices equal
`[(3x+7,5),(y+1,2-3x)],[(0,y-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)`

Options

A. `x= -(1)/(3), y=7`
B. Not possible to find
C. `y=7, x= -(2)/(3)`
D. `x= -(1)/(3), y= -(2)/(3)`

Answer

To solve the problem, we need to equate the corresponding elements of the two matrices given:

Matrix 1:
\[ \begin{pmatrix} 3x + 7 & 5 \\ y + 1 & 2 - 3x \end{pmatrix} \]

Matrix 2:
\[ \begin{pmatrix} 0 & y - 2 \\ 8 & 4 \end{pmatrix} \]

### Step 1: Set up the equations from the matrix elements

From the matrices, we can set up the following equations based on the equality of corresponding elements:

1. \(3x + 7 = 0\) (from the first element)
2. \(5 = y - 2\) (from the second element)
3. \(y + 1 = 8\) (from the third element)
4. \(2 - 3x = 4\) (from the fourth element)

### Step 2: Solve the first equation

From the first equation:
\[ 3x + 7 = 0 \]
Subtract 7 from both sides:
\[ 3x = -7 \]
Now, divide by 3:
\[ x = -\frac{7}{3} \]

### Step 3: Solve the second equation

From the second equation:
\[ 5 = y - 2 \]
Add 2 to both sides:
\[ y = 5 + 2 = 7 \]

### Step 4: Solve the third equation

From the third equation:
\[ y + 1 = 8 \]
Subtract 1 from both sides:
\[ y = 8 - 1 = 7 \]

### Step 5: Solve the fourth equation

From the fourth equation:
\[ 2 - 3x = 4 \]
Subtract 2 from both sides:
\[ -3x = 4 - 2 \]
\[ -3x = 2 \]
Now, divide by -3:
\[ x = -\frac{2}{3} \]

### Step 6: Analyze the results

Now we have two different values for \(x\):
1. From the first equation, \(x = -\frac{7}{3}\)
2. From the fourth equation, \(x = -\frac{2}{3}\)

Since we have two different values for \(x\), it is not possible to find a consistent solution for both \(x\) and \(y\).

### Conclusion

Thus, the answer is that it is not possible to find consistent values for \(x\) and \(y\).

### Final Answer:
b) Not possible to find

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