If`(4x +3,y)=(3x+5,-2)`, then the sum of the values of x and y is

Options

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

Answer

To solve the equation \((4x + 3, y) = (3x + 5, -2)\), we can break it down into two separate equations by equating the corresponding components.

### Step 1: Set up the equations
From the given equation, we can derive two equations:
1. \(4x + 3 = 3x + 5\)
2. \(y = -2\)

### Step 2: Solve for \(x\)
Now, we will solve the first equation for \(x\):
\[ 4x + 3 = 3x + 5 \]
Subtract \(3x\) from both sides:
\[ 4x - 3x + 3 = 5 \]
This simplifies to:
\[ x + 3 = 5 \]
Now, subtract \(3\) from both sides:
\[ x = 5 - 3 \]
Thus, we find:
\[ x = 2 \]

### Step 3: Find the value of \(y\)
From the second equation, we already have:
\[ y = -2 \]

### Step 4: Calculate the sum of \(x\) and \(y\)
Now, we need to find the sum \(x + y\):
\[ x + y = 2 + (-2) \]
This simplifies to:
\[ x + y = 0 \]

### Final Answer
The sum of the values of \(x\) and \(y\) is \(0\).

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