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We can solve this problem using a system of linear equations and then applying matrix methods to find the solution.

### Problem Setup:
Let:
- $ x $ be the amount of money Michael has deposited in the first institution (6% interest).
- $ y $ be the amount of money deposited in the second institution (8% interest).

We are given:
1. $ x + y = 2000 $ (since the total amount is $2000).
2. $ 0.06x + 0.08y = 144 $ (since the total interest earned in a year is $144).

### Step 1: Formulate the system of equations:
\[
\begin{aligned}
x + y &= 2000 \quad \text{(Equation 1)} \\
0.06x + 0.08y &= 144 \quad \text{(Equation 2)}
\end{aligned}
\]

### Step 2: Write in matrix form:
The system of equations can be written in matrix form as:
\[
\begin{pmatrix}
1 & 1 \\
0.06 & 0.08
\end{pmatrix}
\begin{pmatrix}
x \\
y
\end{pmatrix}
=
\begin{pmatrix}
2000 \\
144
\end{pmatrix}
\]

Now, we can solve this system using matrix methods such as Gaussian elimination or using the inverse of the matrix.

Let me solve this.The solution is:

- Michael has \$800 deposited in the institution that pays 6% interest.
- He has \$1200 deposited in the institution that pays 8% interest.

Would you like more details on the steps, or do you have any questions? Here are some related problems for practice:

1. What would the total interest be if the rates were swapped between the two institutions?
2. How much would Michael earn in 2 years with these deposits if the rates remain the same?
3. What if one institution paid 7% instead of 6%? How would the deposits change?
4. If Michael wanted to earn \$200 in interest, how much should he deposit in each institution?
5. How would the solution change if Michael had \$3000 instead of \$2000?

**Tip**: Matrix methods like Gaussian elimination or using inverses are useful for solving linear systems efficiently when you have multiple variables.

Michael Perez has a total of $2000 on deposit with two savings institutions. One pays interest at the rate of 6%/year, whereas the other pays interest at the rate of 8%/year. If Michael earned a total of $144 in interest during a single year, how much does he have on deposit in each institution?

Solve an investment problem where Michael Perez deposits $2000 in two savings accounts with interest rates of 6% and 8%, earning $144 in a year. Learn how to use algebraic and matrix methods to calculate how much is deposited in each account. Suitable for high school students.

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