Final answer:
To solve this problem, we can set up a system of linear equations. We know that $5000 was invested at a 6% annual interest rate, and $18000 was invested at a 7% annual interest rate.
Step-by-step explanation:
To solve this problem, we can set up a system of linear equations. Let's represent the amount invested in the 6% account as x, and the amount invested in the 7% account as y. We know that the total amount invested is $23,000, so we have the equation x + y = 23000. We also know that the total interest earned for the year is $1560, which can be represented by the equation 0.06x + 0.07y = 1560.
To solve this system of equations, we can use the method of substitution or elimination. I will use the method of substitution here. From the first equation, we can solve for x in terms of y: x = 23000 - y. Substituting this expression for x in the second equation, we get 0.06(23000 - y) + 0.07y = 1560. Simplifying this equation, we have 1380 - 0.06y + 0.07y = 1560. Combining like terms, we get 0.01y = 180. Dividing both sides by 0.01, we find y = 18000.
Now, we can substitute this value of y back into the first equation to solve for x: x + 18000 = 23000. Subtracting 18000 from both sides, we find x = 5000.
Therefore, $5000 was invested at a 6% annual interest rate, and $18000 was invested at a 7% annual interest rate.