A system of equations to find the amount invested at each rate are x + y = 18000 and 0.0225x + 0.0425y = 517.
The amount invested at each rate are:
(dollars invested at 2.25%, dollars invested at 4.25%) = (12,400, 5600).
In order to write a system of linear equations to describe this situation, we would assign variables to rate 1 and rate 2, and then translate the word problem into a linear equation as follows:
- Let the variable x represent rate 1.
- Let the variable y represent rate 2.
Based on the information provided about the amount of money invested in two funds. we have the following system of linear equations;
x + y = 18000
0.0225x + 0.0425y = 517
By solving the system of linear equations graphically, we can logically deduce that the solution for this system of linear equations is the point of intersection of each lines on the graph that represents them in quadrant I. Hence, this is represented by the ordered pair (12,400, 5600).
In this context, the pair of linear equation has exactly one solution;
x = $12,400 invested at 2.25%.
y = $5600 invested at 4.25%.