If `4x - 7y = 3 and 2x -y = 9,` then `x -y` is

Options

A. 3
B. 4
C. 5
D. 6

Answer

To solve the system of equations \(4x - 7y = 3\) and \(2x - y = 9\) and find the value of \(x - y\), we can use the elimination method. Here are the steps:

### Step 1: Write down the equations
We have the following two equations:
1. \(4x - 7y = 3\) (Equation 1)
2. \(2x - y = 9\) (Equation 2)

### Step 2: Eliminate one variable
To eliminate \(y\), we can manipulate Equation 2. We will multiply Equation 2 by 7 to make the coefficient of \(y\) the same in both equations.

\[ 7(2x - y) = 7(9) \]
This gives us:
\[ 14x - 7y = 63 \quad \text{(Equation 3)} \]

### Step 3: Subtract the equations
Now we can subtract Equation 1 from Equation 3:
\[ (14x - 7y) - (4x - 7y) = 63 - 3 \]
This simplifies to:
\[ 14x - 4x = 63 - 3 \]
\[ 10x = 60 \]

### Step 4: Solve for \(x\)
Now, we divide both sides by 10:
\[ x = 6 \]

### Step 5: Substitute \(x\) back to find \(y\)
Now that we have \(x\), we can substitute it back into Equation 2 to find \(y\):
\[ 2(6) - y = 9 \]
\[ 12 - y = 9 \]
Subtract 12 from both sides:
\[ -y = 9 - 12 \]
\[ -y = -3 \]
Multiplying both sides by -1 gives:
\[ y = 3 \]

### Step 6: Find \(x - y\)
Now we can find \(x - y\):
\[ x - y = 6 - 3 = 3 \]

Thus, the value of \(x - y\) is \(3\).

### Final Answer:
\[ \text{The value of } x - y \text{ is } 3. \]

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