Solving Two Equations by Elimination

We have seen two methods already that could be employed. However, there is one more method that is at our disposal. The last method for solving linear systems is Elimination.

The Elimination Method is probably the most complicated, but is necessary when dealing with more complex systems. When both equations in a linear system are in the form Ax + By = C, we can solve the system using elimination.

How is this method different from substitution? The idea behind the elimination method is to create a new equation from a combination of the original equations in the system. The new equation is formed by adding or subtracting the originals. When we combine two true equations, the sum or difference must also be true.

Category:

Education

Tags:

• math
• algebra
• linear
• equations
• elimination

[gabriellefreedom2001]

This is all fine and dandy but it doesnt help when you have two y coefficients that are not opposite numbers.

[tqnohe]

@gabriellefreedom2001 If you waited to view this until 3:37, you would see that I address that issue.

[mirosadame]

Thanks so much. This really helped :)

[ssana2016]

I was failing my class u helped me a lot I luv your teachings u should be my teacher my teacher is the worst!! U explained it very clearly thank I am now back to a c+

[Simpsonizer54]

thank you!! that helped!

[thelma787]

these is kinda confusing to me.. i thought you solve it like this: For instance if u have an equation like this:

3x-4y=7.....equation 1

5x-6y=8.....equation 2

No like terms have equal coefficient ..consider the x-term

Their least common multiple is 15

To make these terms equal, multiply equation 1 by 5 and multiply equation 2 by 3

Thus: 5 x equation 1: 5(3x-4y=7) = 15x-20y=35

and; 3 x equation 2: 3(5x-6y=8) = 15x-18y=24.. I don't know if i'm correct tho..it seems you did yours differently :/

[kramarichkids123]

Thank you so much!! You should become a teacher, you actually have personality unlike other people on here..(:

[coty826]

thank you!!!

[tigrisx23]

thanks your doing a good thing here. most of the homework help has to be purchased in bulk and cost something which isnt good for most of us in college paying for everything for school and living. This may be pretty easy but its easy to miss something in class when your life is so busy and your mind wanders at important parts of the discussion.. i can pause and replay and come back when i need to. thank you!

[Prohackroket]

Thank u sooo much :) helped a lot

[jakefoggia124]

THANK YOU SOO MUCH!!!!!! 

[XxAceTrainerGreenxX]

Thank you for clearing my confusion. I was a bit confused when my teacher taught me the elimination method, but I am no longer like that. I am studying for a test tomorrow, and I am hoping I can memorize your methods. Thanks!

[lrmaloney97]

@easynoob123 u dumb ass there not both negative