Problem 85 - College Algebra

Question

What is a system of linear equations? Provide an example with your description.

Step-by-Step Solution

Answer

A system of linear equations is a collection of linear equations involving the same set of variables. An example is \[\begin{{align*}}3x + 2y &= 12, \ x - y &= 1.\end{{align*}}\]

Step 1: Definition of A System of Linear Equations

A system of linear equations (or linear system) is a collection of two or more linear equations involving the same set of variables. For example, with two variables x and y, a linear system is:

Step 2: Giving an Example

An example of a system of linear equations is: \[\begin{{align*}}3x + 2y &= 12, \x - y &= 1.\end{{align*}}\]where x and y are the variables. To satisfy both equations, the values for x and y need to satisfy both conditions, as given by these two equations.

Step 3: Explanation of the Example

In the given example, the system consists of two equations and two variables (x and y). It suggests two conditions for the variables. The first equation states that if 3 units of x are combined with 2 units of y, we get 12 units. The second equation states that if you take one unit of x and subtract one unit of y from it, you get 1 unit. Both conditions must hold true simultaneously.