Answer
Investment in the first fund: $\$11,000$.
Investment in the second fund: $\$9,000$.
Work Step by Step
Let's note the investment in the first fund by $x$.
and the investment in the second fund by $y$.
For the last year:-
Dividend from the first fund $=8\%$ of $x$.
$=0.08x$
Dividend from the second fund $=5\%$ of $y$.
$=0.05y$
The total amount received last year is:
$\Rightarrow 0.08x+0.05y=1330$...... (1)
For this year:-
Dividend from the first fund $=12\%$ of $x$.
$=0.12x$
Dividend from the second fund $=2\%$ of $y$.
$=0.02y$
The total amount received this year is
$\Rightarrow 0.12x+0.02y=1500$...... (2)
Multiply equation (1) by $-2$.
$\Rightarrow -2(0.08x+0.05y)=-2(1330)$
Apply distributive property.
$\Rightarrow -0.16x-0.10y=-2660$ ......(3).
Multiply equation (2) by $5$.
$\Rightarrow 5(0.12x+0.02y)=5(1500)$
Apply distributive property.
$\Rightarrow 0.60x+0.10y=7500$...... (4)
Add equations (3) and (4).
$\Rightarrow -0.16x-0.10y+0.60x+0.10y=-2660+7500$
Add like terms.
$\Rightarrow 0.44x=4840$
Divide both sides by $0.44$.
$\Rightarrow \frac{0.44x}{0.44}=\frac{4840}{0.44}$
Simplify.
$\Rightarrow x=11,000$
Substitute the value of $x$ into equation (1).
$\Rightarrow 0.08(11,000)+0.05y=1330$
Simplify.
$\Rightarrow 880+0.05y=1330$
Subtract $880$ from both sides.
$\Rightarrow 880+0.05y-880=1330-880$
Simplify.
$\Rightarrow 0.05y=450$
Divide both sides by $0.05$.
$\Rightarrow \frac{0.05y}{0.05}=\frac{450}{0.05}$
Simplify.
$\Rightarrow y=9,000$.