If `2x - 5y = 5 and 2x -y = 9,` then x-y is ____

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: Write down the equations
We have two equations:
1. \(2x - 5y = 5\) (Equation 1)
2. \(2x - y = 9\) (Equation 2)

### Step 2: Subtract Equation 2 from Equation 1
We will subtract Equation 2 from Equation 1 to eliminate \(2x\):
\[ (2x - 5y) - (2x - y) = 5 - 9 \]
This simplifies to:
\[ -5y + y = -4 \]
\[ -4y = -4 \]

### Step 3: Solve for \(y\)
Now, divide both sides by -4:
\[ y = 1 \]

### Step 4: Substitute \(y\) back into one of the original equations
We can substitute \(y = 1\) back into Equation 2 to find \(x\):
\[ 2x - 1 = 9 \]
Adding 1 to both sides gives:
\[ 2x = 10 \]
Now, divide by 2:
\[ x = 5 \]

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

### Final Answer
Thus, the value of \(x - y\) is \(4\).

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