Question

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 \( \boxed{24} \).