In this Section:
In this section, we turn to another approach for solving a system of linear equations in two variables. Again we will 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 an algebraic method known as elimination. For this method, we begin by placing each equation in standard form. We then transform one or both equations in such a way that the resulting equations are equivalent and have one pair of variable terms that are opposites. We can then add the left sides and set this equal to the sum of the right sides. The result is a linear equation in one variable. We solve the resulting linear equation in one variable and plug into one of the original equations to find the other unknown. We check our solution by plugging into each original equation. Just as before, we may run across a situation in which we have no solution or an infinite number of solutions.