If `a+b=11 and a-b=7`, then ab=

Options

A. `6`
B. `8`
C. `10`
D. `18`

Answer

To solve the equations \( a + b = 11 \) and \( a - b = 7 \) and find the value of \( ab \), we can follow these steps:

### Step 1: Write down the equations
We have two equations:
1. \( a + b = 11 \) (Equation 1)
2. \( a - b = 7 \) (Equation 2)

### Step 2: Subtract Equation 2 from Equation 1
To eliminate \( b \), we can subtract Equation 2 from Equation 1:
\[ (a + b) - (a - b) = 11 - 7 \]
This simplifies to:
\[ a + b - a + b = 4 \]
\[ 2b = 4 \]
Now, divide both sides by 2:
\[ b = 2 \]

### Step 3: Substitute the value of \( b \) back into Equation 1
Now that we have \( b \), we can substitute it back into Equation 1 to find \( a \):
\[ a + 2 = 11 \]
Subtract 2 from both sides:
\[ a = 11 - 2 \]
\[ a = 9 \]

### Step 4: Calculate \( ab \)
Now that we have both \( a \) and \( b \), we can calculate \( ab \):
\[ ab = 9 \times 2 = 18 \]

### Final Answer
Thus, the value of \( ab \) is \( 18 \).

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