Caleb’s Blog

This week’s Blog post will be about how to solve a system using elimination.

What is elimination?

Elimination is simply a way to solve a system, where the key is a word called zero pairs, which means two numbers which make each other ultimately equal zero. We usually get a zero pair by using multiplication to mold a number into a desired zero pair, but at times we are given equations that are pre-set with a zero pair.

So our first step for using elimination to solve a system, is to of course have our 2 systems preferably in standard form.

Ex:

2x + 3y = 18

4x + 4y =20

The next step is to make a zero pair, and to do this we need to use multiplication to make two numbers a zero pair. In this case, we could multiply the first equation and the second equation to make 3y and 4y a zero pair, but that would be a lot of multiplication and unnecessary work. Instead, we can easily just multiply the first system by -2 to make a zero pair with 4x in the second system.

-2 plugged into 2x+3y=18

=

-4x -6y = -36

4x + 4y = 20

As you can see, -4x and 4x make a zero pair, which is the ultimate goal in using elimination. So after those two numbers eliminate each other, we just add up both equations with their like variabes.

So, we will add

-6y + 4y and -36+20

this will give us

-2y = -16

Now we use division to isolate y, so we will divde both sides by 2

-2y/-2 = -16/-2

this will give us

y=8

Now that we found our base answer, we need to plug in 8 into one of our previous systems

We will use

2x + 3(8) = 18

So the first step is to plug in 8 into y

2x + 3(8) = 18

2x + 24 = 18

after this we want to rearrange the system to add like terms.

2x = 18 -24

2x = -6

Now just like before isolate and divide

2x/2=-6/2

x=-3

This gives us our solved system of (-3, 8) where our two slopes will cross each other.

I chose elimination for this weeks blog post because it is my favorited way to solve a system, and I believed that I could make a well demonstrated blog post on the topic.