If `(x - y)(x + y) = 15 and x + y = 5`, then what is the value of `x//y`?

Options

A. 3
B. 4
C. 5
D. 10

Answer

To solve the equations `(x - y)(x + y) = 15` and `x + y = 5`, we can follow these steps:

### Step 1: Substitute the value of `x + y`
We know that `x + y = 5`. We can substitute this into the first equation:

\[ (x - y)(x + y) = 15 \]

Substituting `x + y`:

\[ (x - y)(5) = 15 \]

### Step 2: Simplify the equation
Now, we can simplify the equation:

\[ 5(x - y) = 15 \]

To isolate `x - y`, divide both sides by 5:

\[ x - y = \frac{15}{5} = 3 \]

### Step 3: Set up the equations
Now we have two equations:

1. \( x + y = 5 \) (Equation 1)
2. \( x - y = 3 \) (Equation 2)

### Step 4: Add the two equations
We can add Equation 1 and Equation 2:

\[ (x + y) + (x - y) = 5 + 3 \]

This simplifies to:

\[ 2x = 8 \]

### Step 5: Solve for `x`
Now, divide both sides by 2 to find `x`:

\[ x = \frac{8}{2} = 4 \]

### Step 6: Substitute `x` back to find `y`
Now that we have the value of `x`, we can substitute it back into Equation 1 to find `y`:

\[ 4 + y = 5 \]

Subtract 4 from both sides:

\[ y = 5 - 4 = 1 \]

### Step 7: Calculate `x/y`
Now we can find the value of `x/y`:

\[ \frac{x}{y} = \frac{4}{1} = 4 \]

### Final Answer
Thus, the value of \( \frac{x}{y} \) is **4**.

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