please see attachment file
Lets say that $\displaystyle x$ is first type of shares and $\displaystyle y$ is second type of shares.
So you can buy total shares:
$\displaystyle \$ 32 \cdot x + \$ 23 \cdot y = \$ 10100$
In order to earn $540 you must set following equation:
$\displaystyle \$ 1.20 \cdot x + \$1.40 \cdot y = \$ 540$
So you have systems of equations:
$\displaystyle \begin{array}{l}
32x + 23y = 10100 \\
1.20x + 1.40y = 540 \\
\end{array}
$
We solve first equation for $\displaystyle x$:
$\displaystyle x = \frac{{10100 - 23y}}{{32}}$
We susbtitute $\displaystyle x$ in second equation:
$\displaystyle 1.20(\frac{{10100 - 23y}}{{32}}) + 1.40y = 540$
$\displaystyle \begin{array}{l}
\frac{{12120 - 27.6y}}{{32}} + 1.40y = 540 \\
\frac{{12120 - 27.6y + 44.8y}}{{32}} = 540 \\
\frac{{12120 + 17.2y}}{{32}} = 540 \\
12120 + 17.2y = 17280 \\
17.2y = 5160 \\
y = 300 \\
\end{array}
$
We susbtitute $\displaystyle y$ in first equation:
$\displaystyle \begin{array}{l}
32x + 23 \cdot 300 = 10100 \\
32x + 6900 = 10100 \\
32x = 3200 \\
x = 100 \\
\end{array}
$
So solution is that you have to buy 100 shares of $32 and 300 shares of 23$.