Wednesday, March 23, 2016

High School Math Solutions – Systems of Equations Calculator, Elimination

A system of equations is a collection of two or more equations with the same set of variables. In this blog post, we will be focusing on a system of linear equations. A system of linear equations is a collection of two or more linear equations with the same set of variables, meaning the variables are only to the first power and there are no products of variables. There are a couple ways to solve a system of linear equations, but in this blog post we will focus on one method, elimination.


Goal: Eliminate variables until there is one left. How?
  1. Multiply equation by a constant (not zero)
  2. Add/subtract equations together
  3. Plug the calculated value of variable in one of the equations to find value of other variable
  4. Double check your work by plugging the values back into the equation

Tips for 3 equations with 3 variables: 
  1. Eliminate x’s first from the 2nd and 3rd equation
  2. 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):
5x+3y=7
3x-5y=-23
1. Multiply top equation by 3 and the bottom equation by 5
3(5x+3y=7)
5(3x-5y=-23)
To get:
15x+9y=21
15x-25y=-115

2. Subtract
\:\:\quad 15x+9y=21
-     \underline{15x-25y=-115}
\:\:\quad 34y=136
3. Solve for y
34y=136
y=4
4. Plug and chug to get x
5x+3(4)=7
x=-1
5. Double check
3(-1)-5(4)=-23


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,

Leah

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