If `[(x+y,4),(-5,3y)]=[(3,4),(-5,6)]`, then the value of x.

Options

A. 1
B. 5
C. `-2`
D. 0

Answer

To solve the problem, we start with the given equality of the matrices:

\[ [(x+y, 4), (-5, 3y)] = [(3, 4), (-5, 6)] \]

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

### Step 1: Equate the first elements of the first row
From the first row of the matrices, we have:
\[ x + y = 3 \quad \text{(1)} \]

### Step 2: Equate the second elements of the first row
From the second elements of the first row, we have:
\[ 4 = 4 \quad \text{(This is always true and does not provide new information)} \]

### Step 3: Equate the first elements of the second row
From the first elements of the second row, we have:
\[ -5 = -5 \quad \text{(This is also always true)} \]

### Step 4: Equate the second elements of the second row
From the second elements of the second row, we have:
\[ 3y = 6 \quad \text{(2)} \]

### Step 5: Solve for y
From equation (2):
\[ y = \frac{6}{3} = 2 \]

### Step 6: Substitute y back into equation (1)
Now substitute \(y = 2\) into equation (1):
\[ x + 2 = 3 \]

### Step 7: Solve for x
Now, solve for \(x\):
\[ x = 3 - 2 = 1 \]

Thus, the value of \(x\) is:
\[ \boxed{1} \]

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