Answer
$x=18000; y=6000$. There should be $ \$ 18,000$ invested in $3.5 \%$ bonds.
Work Step by Step
Let $x$ and $y$ be the amount invested in $3.5 \%$ and $ 5 \% $ bonds.
Multiply the first equation by $-0.05$ and then add the new equation to equation $2$.
Therefore, the system of two equations is:
$-0.5x-0.5y=-1200 \\ 0.035 x+0.05 y=930$
$-0.5x-0.5y+0.035 x+0.05 y=-1200+ 930$
This yields $x=18000$
Substitute the value of $x$ in the first equation to get the value of $y$.
$18000+y=24000 \implies y=6000 $
Thus, $x=18000; y=6000$. There should be $ \$ 18,000$ invested in $3.5 \%$ bonds.
