If ` 2 x - 5y = 5 and 2x - y = 9 ` then (x - y) is equal to

Options

A. 2
B. 4
C. 6
D. 3

Answer

To solve the equations \( 2x - 5y = 5 \) and \( 2x - y = 9 \) and find the value of \( x - y \), we can follow these steps:

### Step 1: Express \( 2x \) from both equations
From the first equation:
\[ 2x - 5y = 5 \]
We can rearrange it to express \( 2x \):
\[ 2x = 5 + 5y \tag{1} \]

From the second equation:
\[ 2x - y = 9 \]
We can rearrange it to express \( 2x \):
\[ 2x = y + 9 \tag{2} \]

### Step 2: Set the two expressions for \( 2x \) equal to each other
Since both equations equal \( 2x \), we can set them equal:
\[ 5 + 5y = y + 9 \]

### Step 3: Solve for \( y \)
Now, we simplify the equation:
\[ 5y - y = 9 - 5 \]
This simplifies to:
\[ 4y = 4 \]
Dividing both sides by 4 gives:
\[ y = 1 \]

### Step 4: Substitute \( y \) back to find \( x \)
Now that we have \( y \), we can substitute it back into either equation to find \( x \). Using equation (2):
\[ 2x = y + 9 \]
Substituting \( y = 1 \):
\[ 2x = 1 + 9 \]
This simplifies to:
\[ 2x = 10 \]
Dividing both sides by 2 gives:
\[ x = 5 \]

### Step 5: Find \( x - y \)
Now we can find \( x - y \):
\[ x - y = 5 - 1 = 4 \]

Thus, the value of \( x - y \) is \( \boxed{4} \).

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