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 substitution. Substitution is more effective than graphing. It works for very large numbers, very small numbers, and non-integer values. Our method starts by solving either equation for either variable. We then plug in for that variable in the other equation. This will yield a linear equation in one variable. We can then solve that equation and find one of the unknowns of the system. Lastly, we plug in for the known value in either original equation. This will allow us to find the other unknown. It is always good practice to check the result by plugging in the solution to both original equations. Just as with the graphing method, we will encounter systems that have no solution and an infinite number of solutions.