Graphs are wonderful thing in the learning of maths.
Not only does it reflects visual symptom or trend in data collected, it displays, if allowed, beautiful images.
This is possible if you allow you maths juice to go free and create mathematical expressions to your fancy and view them on a graph.
Below I have created one. I visual it as water rippling through a surface (on the top view).
Hope you like this maths art of mine.
NOTE: It is created using trigonometry of circulatory expression.
Here I view a water droplet going down into the centre. It then produces ripples or waves spreading outwards in a circular manner.
Imagination ....
Maths expressing ......
:-)
.
Solving of Simultaneous equations may require one common technique called "Elimination" method.
From the name, we know that it has to eliminate or remove something from the equations.
The target is one selected variable or unknown in the mathematical equations.
However, when approaching this method, you noticed that it involved the subtraction (or addition) of equations.
The question is "Can equations be subtracted?".
And "What is the real meaning of subtracting equations?"
My answers:-
Yes, equations can of course be subtracted. Equations are like other items, e.g. apples, chairs.
The real meaning of subtracting equations is not that apparent.
The true and desired wish to subtract equations boils down to commonising a certain coefficient of a variable.
With this common coefficient, it will then be able to remove this mathematical unknown.
(It is not really the direct processing of equations, and the magical removal of variable as a result!)
We commonise the coefficient of the selected variable first before subtracting the equations in order that same items are eliminated.
Hope this clarify some doubts of new learners to simultaneous equations solvers.
Concepts have to be learned upfront without pending questions for complete understanding and smooth follow-up learning in the later stage. Seek to clarify any doubts as far as possible.
It will reduce maths anxiety and allow you to enjoy maths as a result. The reward of clearing any doubts cannot be spelled out in words but through actual working and practice with proper analysis.
I believe you support this notion.
Cheers to maths.
.
