I have two variables, $x$ and $y$, and I want to swap their values. (For example, if $x$ has value 5 and $y$ has value "banana", then after the swap I want $x$ to have value "banana" and $y$ to have value 5.) Explain why the code x = y y = x doesn't work, and figure out what we need to do to swap the values of $x$ and $y$.

see explanation below.

Step-by-step explanation:

I have two variables, $x$ and $y$, and I want to swap their values.

For example, if $x$ has value 5 and $y$ has value "banana", then after the swap I want $x$ to have value "banana" and $y$ to have value 5.

1. Explain why the code x = y y = x doesn't work,

2. figure out what we need to do to swap the values of $x$ and $y$.

1. the code x=y means a copy of the y-value ("banana") to x

after this step, both variables x and y will have the value "banana".

Evidently the next step y=x will recopy the copied value of "banana" in x back to y.

Net result, both variables will contain "banana", not an exchange.

2. The code that will work requires a third temporary variable, say t.

We can then do a circular copy, starting with assignment of t.

t=x   (t now contains 5)

x=y  (x now contains "banana")

y=t   (y now contains 5)

Thus the exchange is now complete.