Elimination method review (systems of linear equations) (article) | Khan Academy (2024)

The elimination method is a technique for solving systems of linear equations. This article reviews the technique with examples and even gives you a chance to try the method yourself.

Want to join the conversation?

Log in

  • Olivia

    8 years agoPosted 8 years ago. Direct link to Olivia's post “what if you are using thr...”

    what if you are using three variables and you have three different equations?
    for example: (three variables,three equations)
    x-y-2z=4
    -x+2y+z=1
    -x+y-3z=11

    (57 votes)

    • Hamza Usman

      4 years agoPosted 4 years ago. Direct link to Hamza Usman's post “First of all, the only wa...”

      Elimination method review (systems of linear equations) (article) | Khan Academy (4)

      Elimination method review (systems of linear equations) (article) | Khan Academy (5)

      Elimination method review (systems of linear equations) (article) | Khan Academy (6)

      First of all, the only way to solve a question with 3 variables is with 3 equations. Having 3 variables and only 2 equations wouldn't allow you to solve for it. To start, choose any two of the equations. Using elimination, cancel out a variable. Using the top 2 equations, add them together. That results in y-z=5. Now, look at the third equation and cancel out the same variable that you originally cancelled out. In this case, we canceled out x. Adding the first equation to the 3rd equation would get rid of his. Adding would give -5z=15. We got lucky because both the x and the y cancelled out. If they didn't both cancel out, you would just have t solve the two equations which you should know how to do. Back to the problem, -5z=15, so z=-3.Plug that into the equation y-z=5 to solve for y. y-(-3)=5, so y+3=5. That gives y=2. Plug both of those into any of the three original equations and solve for x. You get x=0. Your final solution is x=0, y=2, and z=-3 or (0,2,-3).

      (54 votes)

  • 8008161

    6 years agoPosted 6 years ago. Direct link to 8008161's post “What if the numbers befor...”

    What if the numbers before x and y can not make up?

    4x-3y=8
    5x-2y=-11

    (5 votes)

    • Dominic Nguyen

      6 years agoPosted 6 years ago. Direct link to Dominic Nguyen's post “I don't completely unders...”

      Elimination method review (systems of linear equations) (article) | Khan Academy (10)

      Elimination method review (systems of linear equations) (article) | Khan Academy (11)

      I don't completely understand what you mean, but I have an idea of what you're asking. You can multiply both equations by a number to get one of the x or y absolute values the same, multiply the top equation by 2, to get 8x-6y=16, and the second equation by -3 to get -15x+6y=33, then add the equations to get -7x=49, so x is equal to -7. Plug in -7 for x to solve for y which would be -12
      Hope this helps

      (27 votes)

  • Yeyka Rosario

    5 years agoPosted 5 years ago. Direct link to Yeyka Rosario's post “what about unsorted equat...”

    what about unsorted equations?
    -4y-11x=36
    20=-10x-10y

    (7 votes)

    • AD Baker

      5 years agoPosted 5 years ago. Direct link to AD Baker's post “Yeka, Use algebraic man...”

      Elimination method review (systems of linear equations) (article) | Khan Academy (15)

      Yeka,

      Use algebraic manipulation to get the x and y terms on the same side of the =. For the second equation, add 10x to both sides, add 10y to both sides, and subtract 20 from both sides. Then, proceed with the elimination method.

      (10 votes)

  • charlietsmith1010

    4 years agoPosted 4 years ago. Direct link to charlietsmith1010's post “what if you have -14x + 9...”

    what if you have -14x + 9y = 46 and 14x - 9y = 102. Elimination will cancel both x and y out. What do you do?

    (2 votes)

    • Kim Seidel

      4 years agoPosted 4 years ago. Direct link to Kim Seidel's post “You are correct, both the...”

      Elimination method review (systems of linear equations) (article) | Khan Academy (19)

      You are correct, both the X and Y cancel out leaving you with: 0=148. This is a false statement. It is telling you that the system has no solution. It also means that the 2 lines are parallel. Parallel lines have no points in common which is why the system has no solution.
      Hope this helps.

      (14 votes)

  • kesvibp0208

    3 years agoPosted 3 years ago. Direct link to kesvibp0208's post “kesvi patel are we suppo...”

    kesvi patel
    are we supposed to do last divide step ?

    (4 votes)

    • Rin

      3 years agoPosted 3 years ago. Direct link to Rin's post “After you add/subtract th...”

      After you add/subtract the new equations, you eliminate one of the variables and divide. After solving one of them, plug your solved variable to one of the original problems.
      This might help you understand more clearly:

      12x + 2y = 90 ... (1)
      6x + 4y = 90 ... (2)

      (2)*2 12x + 8y = 180 ... (2)'

      (1)-(2)' 12x + 2y = 90
      - 12x + 8y = 180
      -6y = -90
      You eliminated x
      and now you solve y by dividing.
      y = 15
      y = 15 plugged into (2). (Always pick the easier problem to solve your problem accurately.)
      6x + 4(15) = 90
      6x + 60 = 90
      6x = 90 - 60
      6x = 30
      x = 5

      Your final answer will be
      (x,y) = (5,15)

      Hope this helps!

      (9 votes)

  • Noa B

    a year agoPosted a year ago. Direct link to Noa B's post “I don't understand how we...”

    I don't understand how we can do anything to the equasions 10y - 11x = -4 and -2y + 3x = 4!!
    and every time I do this, it marks me wrong for trying to multiply the 3 and -11. And the hint doesn't help either!

    (2 votes)

    • Kim Seidel

      a year agoPosted a year ago. Direct link to Kim Seidel's post “You should multiply by 3 ...”

      You should multiply by 3 and +11 to create -33x and +33x. You need opposite signs to eliminate the x. By using -11, you are making the x terms have the same sign and when you add the 2 equations, no variable is eliminated.

      Try that and see how it works out.
      Comment back with your work if you still have issues.

      (9 votes)

  • alise.blanton

    8 months agoPosted 8 months ago. Direct link to alise.blanton's post “In an honors class in 8th...”

    In an honors class in 8th grade, I am generally confused. Can someone maybe give me the steps in a simple worded form?

    (3 votes)

    • E. Bird {S/H}

      8 months agoPosted 8 months ago. Direct link to E. Bird {S/H}'s post “Well, it depends on what ...”

      Well, it depends on what you need. lets go with the equations:

      10y-11x=-4
      -2y+3x=4

      For this, you want to first make the bottom equation have an equivalent value for one of the variables so that we can eliminate it. the bottom equation is perfect, because:

      -2y(5)+3x(5)=4(5)
      this makes -10y+15x=20

      which in that case...

      10y-11x=-4
      -10y+15x=20
      =
      4x=16
      4x/4=16/4
      x=4

      from there, substitute 4 for x to solve for y, and you have your coordinate variables.

      (7 votes)

  • Zainab

    4 years agoPosted 4 years ago. Direct link to Zainab's post “Do you always have to eli...”

    Do you always have to eliminate the x term?

    (3 votes)

    • Kim Seidel

      4 years agoPosted 4 years ago. Direct link to Kim Seidel's post “No, you can pick the one ...”

      No, you can pick the one that looks like it is the easiest to eliminate.

      (5 votes)

  • Omelette Kai

    5 years agoPosted 5 years ago. Direct link to Omelette Kai's post “when plugging in... do i ...”

    when plugging in... do i plug in to the original equation or the (new) equivalent equation?

    (3 votes)

    • Rohan Mukhija

      3 years agoPosted 3 years ago. Direct link to Rohan Mukhija's post “The new equivalent equati...”

      The new equivalent equation would be plugged in because then you will be able to solve for one of the variables. Then, you can plug that variable into the equation, and then solve for the last one using algebraic manipulation.

      (2 votes)

  • pineapple282

    9 months agoPosted 9 months ago. Direct link to pineapple282's post “Why can't you subtract on...”

    Why can't you subtract one equation from another to eliminate variables?

    (2 votes)

    • Kim Seidel

      9 months agoPosted 9 months ago. Direct link to Kim Seidel's post “You can. You would get t...”

      You can. You would get the same result if it's done correctly. A common error when subtracting the equations is that some signs get changed and others don't. So, the wrong result is created. Most people get fewer errors if they set up the signs first and then add the equations.

      (6 votes)

Elimination method review (systems of linear equations) (article) | Khan Academy (2024)
Top Articles
Latest Posts
Article information

Author: Fr. Dewey Fisher

Last Updated:

Views: 6216

Rating: 4.1 / 5 (62 voted)

Reviews: 85% of readers found this page helpful

Author information

Name: Fr. Dewey Fisher

Birthday: 1993-03-26

Address: 917 Hyun Views, Rogahnmouth, KY 91013-8827

Phone: +5938540192553

Job: Administration Developer

Hobby: Embroidery, Horseback riding, Juggling, Urban exploration, Skiing, Cycling, Handball

Introduction: My name is Fr. Dewey Fisher, I am a powerful, open, faithful, combative, spotless, faithful, fair person who loves writing and wants to share my knowledge and understanding with you.