Example

Solving a Loan Interest Application Using a System of Equations

We can also find the principal amounts of different loans given the total interest by translating the problem into a system of equations. For instance, if the total principal owed on a bank loan bb and a federal loan ff is $ 21,54021{,}540, and the bank loan has a 10.5%10.5\% interest rate while the federal loan has a 5.9%5.9\% rate, with a total paid interest of $ 1,669.681{,}669.68, the system is:

  1. The Principal equation: b+f=21,540b + f = 21{,}540.
  2. The Interest equation: 0.105b+0.059f=1,669.680.105b + 0.059f = 1{,}669.68. Solving this system using substitution provides the principal for each loan.

0

1

Updated 2026-05-25

Contributors are:

Who are from:

Tags

OpenStax

Intermediate Algebra @ OpenStax

Ch.4 Systems of Linear Equations - Intermediate Algebra @ OpenStax

Algebra

Related
Learn After