If `9x - 6y = 15 and x + 6y = 15,` then the value of x.y.

Options

A. `3.4`
B. `3.2`
C. `4.5`
D. `5.6`

Answer

To solve the equations \(9x - 6y = 15\) and \(x + 6y = 15\) for the values of \(x\) and \(y\), and then find the product \(x \cdot y\), we can follow these steps:

### Step 1: Write down the equations
We have two equations:
1. \(9x - 6y = 15\) (Equation 1)
2. \(x + 6y = 15\) (Equation 2)

### Step 2: Add the two equations
To eliminate \(y\), we can add both equations together:
\[ (9x - 6y) + (x + 6y) = 15 + 15 \]
This simplifies to:
\[ 10x = 30 \]

### Step 3: Solve for \(x\)
Now, divide both sides by 10:
\[ x = \frac{30}{10} = 3 \]

### Step 4: Substitute \(x\) back into one of the equations to find \(y\)
We can use Equation 2 for this:
\[ x + 6y = 15 \]
Substituting \(x = 3\):
\[ 3 + 6y = 15 \]
Now, subtract 3 from both sides:
\[ 6y = 15 - 3 \]
\[ 6y = 12 \]

### Step 5: Solve for \(y\)
Now, divide both sides by 6:
\[ y = \frac{12}{6} = 2 \]

### Step 6: Calculate the product \(x \cdot y\)
Now that we have \(x = 3\) and \(y = 2\), we can find the product:
\[ x \cdot y = 3 \cdot 2 = 6 \]

### Final Answer
The value of \(x \cdot y\) is \(6\).

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