the sum of the real numbers x and y is 11 their difference is 5 what is the value of xy

Answer 1

We can solve the problem using a system of equations based on the given conditions:

1. The sum of \( x \) and \( y \): \[ x + y = 11 \]

2. The difference of \( x \) and \( y \): \[ x - y = 5 \]

Now we can solve this system of equations.

First, we can add the two equations:

\[ (x + y) + (x - y) = 11 + 5 \]

This simplifies to:

\[ 2x = 16 \]

Dividing both sides by 2 gives:

\[ x = 8 \]

Next, we can substitute \( x = 8 \) back into the first equation to find \( y \):

\[ 8 + y = 11 \]

Solving for \( y \) gives:

\[ y = 11 - 8 = 3 \]

Now we have \( x = 8 \) and \( y = 3 \). To find the value of \( xy \):

\[ xy = 8 \times 3 = 24 \]

Therefore, the value of \( xy \) is \( \boxed{24} \).