$x=18000; y=6000$. 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.