Let x be the amount (in dollars) invested in bond A and y be the amount (in dollars) invested in bond B.
According to the given information, the investor has to invest a total of $50,000, so we have the equation:
x + y = 50000 ----(1)
The return on investment for bond A is 5%, which can be expressed as 0.05x. Similarly, the return on investment for bond B is 10%, which can be expressed as 0.10y.
The total return on investment is $3,750, so we have the equation:
0.05x + 0.10y = 3750 ----(2)
Rewriting equation (2) by multiplying both sides by 100 to eliminate the decimals, we get:
5x + 10y = 375000 ----(3)
The system of equations to represent this problem can be written as:
x + y = 50000
5x + 10y = 375000
Writing the system of equations as a matrix equation, we have:
[A] * [x; y] = [B], where
[A] = [[1 1]; [5 10]],
[x; y] = [[x]; [y]],
[B] = [[50000]; [375000]].