`[{:(2x+y,4x),(5x-7,4x):}]=[{:(7,7y-13),(y,x+6):}]` then the value of `x,y` is

Options

A. x =3,y=1
B. x=2,y=3
C. x=2,y=4
D. x=3,y=3

Explanation

To solve the equation given in the question, we start by equating the corresponding elements of the two matrices.

The equation is:

\[ \begin{pmatrix} 2x + y & 4x \\ 5x - 7 & 4x \end{pmatrix} = \begin{pmatrix} 7 & 7y - 13 \\ y & x + 6 \end{pmatrix} \]

### Step 1: Equate the corresponding elements

From the first row and first column, we have:

\[ 2x + y = 7 \quad \text{(Equation 1)} \]

From the first row and second column, we have:

\[ 4x = 7y - 13 \quad \text{(Equation 2)} \]

From the second row and first column, we have:

\[ 5x - 7 = y \quad \text{(Equation 3)} \]

From the second row and second column, we have:

\[ 4x = x + 6 \quad \text{(Equation 4)} \]

### Step 2: Solve Equation 4 for x

From Equation 4:

\[ 4x = x + 6 \]

Subtract \(x\) from both sides:

\[ 4x - x = 6 \]

This simplifies to:

\[ 3x = 6 \]

Now, divide both sides by 3:

\[ x = 2 \]

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

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

\[ 2(2) + y = 7 \]

This simplifies to:

\[ 4 + y = 7 \]

Subtract 4 from both sides:

\[ y = 3 \]

### Step 4: Conclusion

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

\[ x = 2, \quad y = 3 \]

### Final Result

The final answer is:

\[ (x, y) = (2, 3) \]

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