•´¯`•. ĊŖÄMËŖ'Ś ŖŮĻË .•´¯`•

 Greetings, fellow visitors of Mathland. 

I humbly welcome you to our newly created attraction - Cramer's Land.

In this park, we will be discussing and enjoying the simplicity and efficiency of solving for variables.

Starting off, for Cramer's Rule, there are three different variations of it.

Dx/D, Dy/D, and Dz/D

The D in the denominator represents the determinant while the Dx, Dy, and Dz, represent the matrices "row x/y/z" replaced with the solution (number after the equal sign) placed in the numerator. Once you find all the answers, you merely divide the numerator by the demons stir and you will get the answer for each variable. To check to see if you have done it right, plus the numbers back into one of the original equations and if it solves to the answer given, then you have solved the problem correctly.

Overall, using Cramer's Rule allows for one to easily find the answer to the numerical values of the digits.

I do hope you enjoyed your time here and learned a few things.~

Good day and farewell, dear guests!

׺°”˜`”°º× ѕуѕтємѕ σf єqυαтισиѕ ×º°”˜`”°º×

Hello fellow individuals of Mathland!

It has been some time since I last came upon you!

Why don't we have a short chat to reacquaint ourselves?~

I actually looked forward to introducing you all to a new topic, called System of Equations. 

Shall we begin?~

System of equations are two or three given equations with variables. In order to solve these, one must find what numbers the variables are. There are two ways in solving such a problem.

Here are 2 ways:

As you can see, both are able to be used. 

Also in solving system of equations, one has to take into consideration of the problem being either inconsistent or consistent.

Inconsistent means that there are no solutions, and if graphed, the lines would be parallel.

Consistent means that there is 1 solution (independent) or an infinite amount of solutions (dependent).

Below is an example, of a "system of equation problem" with three equations.

Well, that will be all for now! I do hope you enjoyed our discussion. 

Farewell.~

My Polar Equation Graph

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Hello, dear ladies and gentlemen of Mathland.

Today we will be having a free day among'st ourselves to explore wherever you would like to go. For those who would like to journey with me,  I will be making a delivery to the Singing Flower Garden. Along the way I will be talking about polar coordinates.

Choose wisely young ones.~

Well, lovely to have those of you who joined me for company. I give many thanks.

Now moving along.~ 

Polar equations are quite different from the usual way in graphing. 

Unlike the Cartesian Plane, the Polar Graph's shape is slightly varied. 

While the Cartesian Plane graphs points with the coordinates of (x,y) =, the polar plane graphs points using (r, θ).

Notes:

However, if one is confused, there are ways to transition between polar to rectangular and rectangular to polar coordinates. 

For polar to rectangular, one uses two equations:

x=rcos(θ)

y=rsin(θ)

For rectangular to polar:

r²=x²+y²

tan(θ)=y/x

Notes:

An important note for the theta, is that if it is greater then zero, then the graph will go counterclockwise, and if the theta is less than a zero, then the graph will go clockwise.

~~~~~~~~~~~~~~

Thank you for accompanying me on my visit to the Singing Flower garden and listening to my lecture.~

Farewell, ladies and gentlemen.

See you soon.~