Here you’ll learn the final method for solving a system of equations, the elimination method. Below are the instructions for how to use this method, followed by an example of solving a system of equations with this method.
Rule
The Elimination Method
- 1.
- Choose a variable that will be eliminated.
- 2.
- Multiply the equations and by the numbers that would make the variable you chose have the same coefficient, but with opposite signs. This will allow you to cancel them.
- 3.
- Write the new equations below the first two.
- 4.
- Add equation to equation , and write the answer below these equations. Now, you’re left with one equation, with one unknown. Solve it.
- 5.
- Put the answer you find into equation , and solve for the final variable.
- 6.
- Write your answer using coordinates:
ANSWER:
Example 1
Solve the system of equations
- 1.
- Let’s decide to get rid of .
- 2.
- Since you have in equation and in equation , you have to multiply equation by to eliminate . In this case, you don’t have to multiply equation by anything:
- 3.
- Write the two equations again after applying the changes:
- 4.
- Add the two equations together such that is eliminated, and solve for :
- 5.
- Put the answer into either equation or . Here, you can choose whichever you like. Let’s pick equation in this case:
- 6.
- Write the answer using coordinates:
ANSWER:
