If `[(x+y,1),(2y,5)]=[(7,1),(4,5)]` find 'x'

Answer

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

\[ \begin{pmatrix} x+y & 1 \\ 2y & 5 \end{pmatrix} = \begin{pmatrix} 7 & 1 \\ 4 & 5 \end{pmatrix} \]

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

From the equality of the matrices, we can write the following equations:

1. \( x + y = 7 \) (from the first row, first column)
2. \( 1 = 1 \) (from the first row, second column, which is always true)
3. \( 2y = 4 \) (from the second row, first column)
4. \( 5 = 5 \) (from the second row, second column, which is also always true)

### Step 2: Solve for \( y \)

From the equation \( 2y = 4 \):

\[ y = \frac{4}{2} = 2 \]

### Step 3: Substitute \( y \) back into the first equation to find \( x \)

Now, substitute \( y = 2 \) into the equation \( x + y = 7 \):

\[ x + 2 = 7 \]

### Step 4: Solve for \( x \)

Subtract \( 2 \) from both sides:

\[ x = 7 - 2 = 5 \]

### Final Answer

Thus, the value of \( x \) is \( 5 \).

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