How is Cramer's rule used in life?

Answer 1

Cramer's Rule is used to solve systems of linear equations by converting those equations into one matrix equation. For example:

ax + by = e

cx + dy = f

becomes

|a bx|=|e|

|c dy| |f|

An example that I came up with just yesterday involved cell phone bills. It looked something like this:

Cindy and Suzi just received their cell phone bills. They have the same provider and can see how many minutes they used and text messages, but they are curious to how much each text message and a single minute costs. Cindy's bill tells her that she used

638 text messages and 230 minutes for a total of $42. Suzi's bill showed that she used 290 text messages and 540 minutes for a total of $29. How much does a text message cost and how much does each minute cost?

To solve this question, you would set up the information given above into two equations:

638x + 230y = 42

290x + 540y = 29

where x is the cost of one text message and y is the cost of one minute used.

There are a lot of other examples in real life that you can set up like the following equations.

Answer 2

It is used for solving a system of linear equations where the number of equations equals the number of variables - and it is known that there is a unique solution.