Answer
Klimt's work: $\$135$ million
Picasso's work: $\$104$ million
Work Step by Step
Let's note:
$k$=the price of Klimt's work
$p$=the price of Picasso's work
We can write the system of equations:
$\begin{cases}
k+p=239\\
k-p=31
\end{cases}$
Add the two equations to eliminate $p$ and determine $k$:
$k+p+k-p=239+31$
$2k=270$
$k=\dfrac{270}{2}$
$k=135$
Substitute the value of $k$ in the first equation to determine $p$:
$k+p=239$
$135+p=239$
$p=239-135$
$p=104$
