Introduction

In my previous post, we got to know this tool, GeoGebra. But what is the magic of it? How can it help us to avoid draining the brain? Today, let me use some examples to show how to use it solving equations.

Solve Linear Equations with One Variable

Let's look at a simple linear equation first:
5x + 3 = 8.
Basically, it is easy to know that the answer is:
x = (8 - 3) / 5 = 1
Let's look at how Geogebr does the tricks. All you have to do is typing the function into the working area and clicking the 'SOLVE" button. Here we go.

Pretty cool! Right?

Solve System of Linear Equations with Two Variables

Some of you might think the first example is too simple for using a solftware to solve it. Ok, let's look at a system of linear equations. I guess not many of you guys are able to solve it by your mind. Here is the original problem and how we solve it manually:

3x + 5y = 11 (A) 3A+5B => 34x=68 => x=68/34=2
5x - 3y = 7 (B) 5A-3B => 34y=34 => x=34/34=1

Similarily, we type it into the working area of Geogebra and click the "SOLVE" button. As shown in the images below, we got the correct answer again.

Yes!

Solve Quadratic Equations

Moving on to a even more complicated problem. here we got:
x ² - 3x + 2 = 0.

If we solve it manually, it will be (x - 1) (x - 2) = 0, therefore, we got
x = {1, 2}.

Let's look at how Geogebra got. The details are shown in the folloiwng images.

Beautiful!

Solve Factorization

As you have seen, Geogebra is pretty powerful and handy for solving vaiours equations. Next, I will teach you an even more cool fuction of it. Ta-da, it can be applied to do factorizaitons. Can you imagine that? :-)

The original problem is as follows:

x² - 3x + 2

Again, to prove the anser, first we solve it manually. It is easy to know that the answer is:

(x - 1) (x - 2).

Now let's look at what Geogebra will give us. Please refer to the following image for details.

Saved the day, as always! Now I can save time for coffee! What about you?