Lesson 4: Solving Linear Systems by Elimination
Module 7: Systems of Linear Equations
Lesson 4 Summary
In this lesson you investigated the following questions:-
In using the elimination method, how do you know whether equations need to be multiplied, added, or subtracted?
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How does adding or subtracting the equations of a linear system affect the solution to the system?
In this lesson you learned how to use the elimination method to solve systems of linear equations. This method is based on the properties of linear systems. The first property is that the solution to a linear system is unchanged when the equations in the system are either added or subtracted. The second property is that the solution is also unchanged when any equation in the system is multiplied by a constant. You discovered these properties when you graphed the sum, difference, and multiples of the linear equations. In doing so, you saw that the graphs passed through the same point of intersection as the original equations in the system.
To use the elimination method successfully, you learned that you have to match the coefficients of either the x-term or the y-term. You can do this by multiplying one or both equations by a constant. Once the coefficients match, you can either add or subtract the two equations in order to eliminate the term. If the matching coefficients have opposite signs, you would add the equations. However, if the matching coefficients have the same signs, then you would subtract the equations. The result is a simplified equation that can be solved for the remaining variable.
Did you know that a linear system can have different numbers of solutions? In the next lesson you will investigate the number of solutions of a linear system. In the last lesson of this module you will use the elimination method as a strategy in solving context-based problems. You will also make decisions about which solution strategy is the most appropriate in specific situations.