In this Section:
In this section, we review the concept of solving a system of linear equations in two variables. In this section, we will only look at systems with two equations and two variables (x and y). When we solve a linear system in two variables, we are looking for any ordered pair that works as a solution to each equation of the system. For the majority of systems, we are looking for one ordered pair. In special case scenarios, there could be no solution or an infinite number of solutions. Here we will focus on the most basic method for solving a system of linear equations in two variables. We will have a refresher on how to solve this type of system using graphing. Recall from algebra 1, this method is tedious and does not produce clear results when numbers are very large, very small, or non-integers. Essentially, we will graph each equation of the system separately, then look for the point of intersection. Since each point on a given line is a solution to that equation, the point of intersection lies on both lines and therefore satisfies both equations. This would be our solution for the system. We will also discuss the special case scenarios. When we come across two parallel lines, there will never be a point of intersection. This type of system is said to be inconsistent, and there is no solution. We will also come across a scenario, where we are presented the same line twice. In this situation, there are an infinite number of solutions.