How Can We Solve Systems of Equations?
Substitution Method
What is it?
Video on Substitution Source: [Shmoop]. (2013, June 11). Solving systems of equation by substitution by Shmoop. [video file]
Best used when one of the equations is solved for a variable making it easier to know which one to substitute.
Elimination Method
What is it?
When do we use it?
Examples
Graphing
Best used when both equations are solved for y. You can always solve for y to graph. If the solution is a fraction, you may have difficulty seeing the exact answer on a graph.
Lesson on Mathplanet with video examples CC-BY-NC-ND 4.0
It is a way to visually represent both equations on a coordinate plane so you can see the solution (where the lines intersect). Image Source: CoolMath. "Solving by Graphing." Cool Math. Constructive Media, 2017. Web. 5 June 2017.
What is it?
Two equations with two variables (typically x and y) that share a common answer. Sometimes an answer does not exist.
What is the goal?
To find the ordered pair (x, y) that is a solution to both equations at the same time.
OpenAlgebra Website with Examples
CC-BY-NC-SA 3.0
Best used when the equations are both in standard form. You may or may not have to multiply one or both equations to make something cancel.
It is a way to solve systems by combining the two equations with addition or subtraction to cancel out one of the two variables. This will allow you to solve for the other variable.
It is a way to solve systems by plugging in one equation in place of a variable of another equation and solving like a multi-step equation from previous chapters.
Examples
What is it?
When do we use it?
Examples
When do we use it?