Answer
$500$ dollars in the $6\%$ account and $2500$ dollars in the $8\%$ account.
Work Step by Step
Step 1. Assume $x$ dollars are invested in the $6\%$ account and $y$ dollars are invested in the $8\%$ account.
Step 2. Based on the given conditions, we have $\begin{cases} x+y=3000\\0.06x+0.08y=230 \end{cases}$
Step 3. Rewrite the system of equations as $\begin{cases} 6x+6y=18000\\6x+8y=23000 \end{cases}$
Step 4. Take the difference between the two equations; we have $2y=5000$ and $y=2500$ dollars.
Step 5. Thus we have $x=500$ and $y=2500$ dollars.
