Goal: Eliminate variables until there is one left. How?
- Multiply equation by a constant (not zero)
- Add/subtract equations together
- Plug the calculated value of variable in one of the equations to find value of other variable
- Double check your work by plugging the values back into the equation
Tips for 3 equations with 3 variables:
- Eliminate x’s first from the 2nd and 3rd equation
- Eliminate y in 3rd equation
It’s easier to visually understand elimination. We will go through one example step by step.
Here’s an example (click here):
1. Multiply top equation by 3 and the bottom equation by 5
3. Solve for y
4. Plug and chug to get x
5. Double check
Here’s another example with two equations (click here):
Here’s an example of three equations with three variables (click here):
*Remember to use the tips for solving this type of system of linear equations!
Solving a system of equations using elimination is pretty simple. Keep your work clean, double check your work for small errors, and practice a couple problems. Elimination is a very popular method to solve systems of linear equations before learning about matrices, so it is important to practice it.
Until next time,