Formulate a system of equations for the situation below and solve.

Michael Perez deposited a total of $3000 with two savings institutions. Bank A pays interest at the rate of 6%/year, whereas Bank B pays interest at the rate of 7%/year. If Michael earned a total of $194 in interest during a single year, how much did he deposit in each institution?
Bank A $

Bank B $

Let's assume Michael deposited x amount of dollars in Bank A and y amount of dollars in Bank B.

Based on the information given, we can create the following system of equations:

Equation 1: The interest earned from Bank A at a rate of 6%/year
0.06x

Equation 2: The interest earned from Bank B at a rate of 7%/year
0.07y

Equation 3: The total interest earned of $194
0.06x + 0.07y = 194

We also know that the total amount deposited by Michael is $3000, so we can create another equation:

Equation 4: The total amount deposited
x + y = 3000

We now have a system of linear equations:

0.06x + 0.07y = 194
x + y = 3000

We can solve this system of equations using various methods, such as substitution or elimination. Let's use the elimination method to solve it.

To eliminate the decimal points, we can multiply both sides of the first equation by 100:

6x + 7y = 19400

Now, we can rewrite the system of equations:

6x + 7y = 19400
x + y = 3000

To solve the system, we can multiply the second equation by 6 and subtract it from the first equation:

6x + 7y - 6x - 6y = 19400 - 18000
y = 1400

Substituting the value of y back into the second equation:

x + 1400 = 3000
x = 3000 - 1400
x = 1600

Therefore, Michael deposited $1600 in Bank A and $1400 in Bank B.

To solve this problem, let's assign variables to the unknowns and set up a system of equations.

Let's say the amount of money Michael deposited in Bank A is x dollars and the amount he deposited in Bank B is y dollars.

The interest earned from Bank A at a 6% interest rate can be calculated as: 0.06x (since 6% = 0.06 as a decimal).

The interest earned from Bank B at a 7% interest rate can be calculated as: 0.07y (since 7% = 0.07 as a decimal).

Since Michael earned a total of $194 in interest, we can set up the following equation:
0.06x + 0.07y = 194

We can also set up another equation to represent the total amount deposited by Michael:
x + y = 3000

Now we have a system of equations:

Equation 1: 0.06x + 0.07y = 194
Equation 2: x + y = 3000

We can solve this system of equations by substitution, elimination, or matrix methods. Here, we will use the substitution method.

From Equation 2, we can rewrite it as x = 3000 - y.

Substituting this value of x into Equation 1, we get:
0.06(3000-y) + 0.07y = 194

Simplifying further:
180 - 0.06y + 0.07y = 194
0.01y = 14
y = 1400

Now substitute the value of y back into x = 3000 - y:
x = 3000 - 1400
x = 1600

Therefore, Michael deposited $1600 in Bank A and $1400 in Bank B.

If x is at 6%, then the rest y=(3000-x) is at 7%. So,

x+y = 3000
.06x + .07y = 194.00