$x=20,000; y=12000$. There should be $ \$ 20,000$ invested in $5.75 \%$ bonds.
Work Step by Step
Let $x$ and $y$ be the amount invested in the $5.75 \%$ and $ 6.25 \% $ bonds. Multiply the first equation by $-0.0625$ and then add the new equation to equation $2$. Therefore, the system of two equations is: $-0.0625x-0.0625y=-2000 \\ 0.0575 x+0.0625 y=1900$ $-0.0625x-0.0625y+0.0575 x+0.0625 y=-2000+1900$ This yields $x=20,000$ Substitute the value of $x$ in the first equation to get the value of $y$. $20,000+y=32000 \implies y=12000 $ Thus, $x=20,000; y=12000$. There should be $ \$ 20,000$ invested in $5.75 \%$ bonds.