What is the elimination method?

Answer 1

The elimination method is a way of solving a system of equations. But rather than solving one equation in terms of a single term and substitution it into the other equations, you use "elimination".

This is accomplished by *adding* or *subtracting* a pair of equations to eliminate at least one variable. Often you will need to multiply one of the expression first to make a term the same, then you can combine them to eliminate the variable.

For example if you had:
2x + 3y = 7
2x - y = 3

Notice you have 2x in both. So if you *subtract* the 2nd equation from the first you will eliminate 2x completely:

Subtracting you get:
3y - (-y) = 7 - 3
4y = 4

Then you can solve for y:
y = 1

Now go back and solve for x using substitution again:
2x + 3(1) = 7
2x = 7 - 3
2x = 4
x = 2

A little harder example would be the following equations:
3x + 5y = 13
2x - 7y = -12

Here none of the terms are the same (or opposites). But if you multiply the top equation by 2, and the bottom equation by 3 you'll get 6x in both:

6x + 10y = 26
6x - 21y = -36

Now you can subtraction the 2nd equation from the first, just like before:

(10 - (-21))y = 26 - (-36)
31y = 62
y = 2

Solve for x (e.g. x = 1).

Answer 2

If you are talking about solving a system of two equations in two unknowns, the elimination method involved modifying one or both equations (if necessary) until the coefficients of one of the variables have the same absolute value, and then either adding the equations (if the coefficients have opposite signs) or subtracting the equations to eliminate one of the variables

1) 2x + 4y = 7

2) 3x + 5y = 14

Here you would multiply eq 1 by 3 and eq 2 by 2 so both coefficients of x = 6 and then subtract one equation from the other thus eliminating the variable x


Alternatively, you could multiply eq 1 by 5 and eq 2 by 4 to eliminate the variable y

Answer 3

For math, it means using 2 different equations together so that one of the variables is eliminated. For example, given
x + 2y = 4 and 3x - 2y = 12
you can add the like terms to eliminate one of the variables like this:
x + 2y = 4
+ 3x - 2y = 12
---------------------
= 4x = 16

Solving for x you get x = 16/4 = 4
Choosing one of the original equations, you can replace x with 4 and solve for y,
3(4) - 2(y) = 12
12 - 2(y) = 12
-2(y) = 0
y = 0.

You now have values for x and y that solve both equations. The values were determined by eliminating the variable in one of the equations.

Answer 4

The elimination method is a method used to solve systems of equations. Here is an example:

2x+5y=15
3x-3y=12

Step 1) Make it so that the coefficients for x or y are the same for both equations, using multiplication of division. We will work with getting x's coefficient equal.

(2x+5y)*3=15*3 --- For the first equation multiply both sides by 3.
(3x-3y)*2=12*2 --- For the second equation multiply both sides by 3

6x+15y=45
6x-6y=24

Now that we have 6x in both equations, we are going to use the if a=b then a-c=b-c rule. Since 6x-6y=24, we can subtract like so:

6x+15y - (6x-6y) = 45 - (24)
21y=21
y=1

An easier way to think of it is just like a subtraction problem

6x+15y=45
-[6x-6y=24]
0x+21y=21
y=1

Then plug in x to one of the original equations to get x=5.

Hope this helped.