Solving Linear Systems Using Substitution
When you do not have a graphing calculator, using tables or graphs is not necessarily the most efficient way to solve a system of equations. If the intersection does not have integral coordinates, using tables or graphing without the aid of a calculator just allows for an approximate or estimated solution.
In those cases, we want to use algebraic methods of substitution and elimination to find an accurate solution to the system. In this resource, we will study substitution.
Substitution Method
Think of the team sports that you have watched or played. One of the coach’s strategies could be to keep the other team off-balance by substituting in new players before the other team can figure out the big game-plan. When substituting, the coach replaces one player with another player in the same position who is (hopefully) of equal value to the team. Well, that is the same thing that we do in mathematics; in substitution, we replace one variable with a number or expression of equal value.
You are going to look at a few video clips to see examples of how systems are solved using substitution.
Source: A17.3 Solving a System of Equations by Substitution, ttor68, YouTube
In this example, one equation is in standard form and the other is in slope-intercept form.
Solving an System of Equations: Substitution
In the following video, watch how 2 different systems of linear equations in standard form are solved using the Substitution Method.