Comparing Methods for Solving Linear Systems
Introduction
Read the information and watch the videos. The beginning provides a nice summary of the main methods for solving systems of equations and when you should use each one. The rest of the article offers a good overview of the different methods and discusses why each method was chosen for a given problem.
There are a number of methods for solving systems of equations, and each has its own strengths. For simplicity, we'll look at them in table form. This should help you decide which method would be best for a given situation.
| Method: | Best used when you... | Advantages: | Comment: |
|---|---|---|---|
| Graphing | ...don't need an accurate answer. | Often easier to see number and quality of intersections on a graph. With a graphing calculator, it can be the fastest method since you don't have to do any computation. | Can lead to imprecise answers with non-integer solutions. |
| Substitution | ...have an explicit equation for one variable (e.g. \(\begin{align*}y = 14x + 2\end{align*}\)) | Works on all systems. Reduces the system to one variable, making it easier to solve. | You are not often given explicit functions in systems problems, so you may have to do extra work to get one of the equations into that form. |
| Elimination by Addition or Subtraction | ...have matching coefficients for one variable in both equations. | Easy to combine equations to eliminate one variable. Quick to solve. | It is not very likely that a given system will have matching coefficients. |
| Elimination by Multiplication and then Addition and Subtraction | ...do not have any variables defined explicitly or any matching coefficients. | Works on all systems. Makes it possible to combine equations to eliminate one variable. | Often more algebraic manipulation is needed to prepare the equations. |
The table above is only a guide. You might prefer to use the graphical method for every system in order to better understand what is happening, or you might prefer to use the multiplication method even when a substitution would work just as well.
Source: cK-12, https://flexbooks.ck12.org/cbook/ck-12-algebra-i-concepts/section/7.6/primary/lesson/comparing-methods-for-solving-linear-systems-alg-i/
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