If (x+y) = 12 and (x-y) = 4 then (2x - 4y) = ?

Options

A. 4
B. 3
C. 2
D. 0

Answer

To solve the problem step by step, we will use the given equations to find the values of \(x\) and \(y\), and then substitute those values into the expression \(2x - 4y\).

### Step 1: Write down the given equations.
We have the following two equations:
1. \(x + y = 12\) (Equation 1)
2. \(x - y = 4\) (Equation 2)

### Step 2: Add the two equations.
To eliminate \(y\), we can add Equation 1 and Equation 2:
\[ (x + y) + (x - y) = 12 + 4 \]
This simplifies to:
\[ 2x = 16 \]

### Step 3: Solve for \(x\).
Now, divide both sides by 2:
\[ x = \frac{16}{2} = 8 \]

### Step 4: Substitute \(x\) back into one of the original equations to find \(y\).
We can use Equation 1:
\[ x + y = 12 \]
Substituting \(x = 8\):
\[ 8 + y = 12 \]
Now, solve for \(y\):
\[ y = 12 - 8 = 4 \]

### Step 5: Substitute \(x\) and \(y\) into the expression \(2x - 4y\).
Now we have \(x = 8\) and \(y = 4\). Substitute these values into the expression:
\[ 2x - 4y = 2(8) - 4(4) \]
Calculating this gives:
\[ = 16 - 16 = 0 \]

### Final Answer:
Thus, the value of \(2x - 4y\) is \(0\).

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