Discussion for Applications of Linear Systems
When solving a system of equations, how do you determine which method to use?
Be sure that you have downloaded the Discussion Guidelines and Discussion Rubric from the Review page of this lesson. Then visit the Applications of Linear Systems Discussion board and post your response to the question. Check back again later to respond to posts that other students have made.
When determining which method to use to solve a system of equations, it is important to consider the number of equations and variables in the system, as well as any special characteristics that may make one method more efficient than another.
For systems of two linear equations in two variables, the most commonly used methods are graphing, substitution, and elimination. Graphing may be a good option when the equations are easily graphable, and the intersection point is easily identifiable. Substitution is useful when one of the equations can be easily solved for one variable, which can then be substituted into the other equation. Elimination is often a good choice when the coefficients of one variable are equal when multiplied by a certain factor.
For systems with more than two equations, the elimination method can become more complex, and matrices or Gaussian elimination may be more efficient ways to solve the system. Matrices are particularly useful when solving large systems of equations, as they can be easily manipulated to solve for the variables.
In summary, the choice of method to solve a system of equations depends on the specific characteristics of the equations and variables involved. It is important to consider the number of equations, variables, and any special characteristics that may make one method more appropriate than another.