When to Use Elimination Method
The elimination method is most efficient when both equations in a system are in standard form and coefficients of one variable are already opposites or can easily be made so through multiplication. Grade 11 students in enVision Algebra 1 (Chapter 4: Systems of Linear Equations and Inequalities) learn to choose elimination over substitution when no equation is already solved for a variable. When one equation is solved for a variable, substitution is typically simpler.
Key Concepts
| Substitution | Elimination | | : | : | | Use when one equation is already solved for one variable. | Use when the equations are in standard form and coefficients can be easily eliminated. |.
Common Questions
When should you use the elimination method to solve a system?
Use elimination when both equations are in standard form (Ax + By = C) and the coefficients of one variable are opposites or can easily be made opposites by multiplying.
When is substitution better than elimination?
Use substitution when one equation is already solved for a variable (like y = 2x + 3), because plugging it directly into the other equation is straightforward.
How do you make coefficients opposite for elimination?
Multiply one or both equations by constants so that the coefficients of one variable are equal in magnitude but opposite in sign, then add the equations.
What is the goal of elimination?
To add the two equations so that one variable cancels (is eliminated), leaving a single equation with one variable that can be solved directly.
Can you always use either substitution or elimination?
Yes. Both methods work for any system of linear equations. The choice is about efficiency based on the form of the equations.
What should you do after eliminating one variable?
Solve for the remaining variable, then use back-substitution to find the value of the eliminated variable.