I Can See The Light!

And no, no. No Lawliet anywhere. Sorry.

However, I could've sworn I almost saw sparkly thingies. 8O

Why? It's algebra. Finals for Advanced Algebra were today. And I studied hard enough to say that I passed through the multiple choice fairly fine, though uncertain, as every student is--except Isaac. But when I got to the final page--actually, when we all got to the final page--all Junior students, not only from my class, but the other class-even Isaac!--were frozen still by the fear of a large blank page haunting them. No answers. Just...questions. Certifiably unanswerable questions.

Well, what was the question?

//WARNING TO EVERYONE WHO HATES MATH AND WILL CERTAINLY HAVE A HEADACHE BECAUSE OF THIS//

There is a package of 24 shapes, consisting of squares, pentagons and hexagons. The sum of all sides of the shapes are 112 sides. And there are 10 more square pieces than there are pentagons. What is the number of pieces of each shape in the package?

Now, normally, an idiot would have broken down and cried reading that question. My classmates managed to endure the question. But died when they found their answers were no-where to be found on the multiple choice.
*Note: All multiple choice questions include solution boxes, and are worth two points combined. If you don't have a solution, or you get the solution wrong, you get no points for either. It's an all or nothing system.

We all froze at the sight of the page staring back at us, mocking us, telling us we were stupid freaks who can't understand numbers, of all things.
As if it was telling us that it is the master over us.
No way.
Our frozen stance broke into frustration, and then firing rage (not raging fire, that's different) which translated into loud complaints and demands for exam extensions. (Which we received, by popular demand. People Power!)

But then the teacher came into the classroom, and wrote on the board, as our proctor watched her. And she wrote on the board that there were corrections:
change "10 squares more than pentagons" to "10 hexagons more than squares".

So we did.

Using the Cramer's Rule of determinants, we lined up the three equations like so:
x + y + z = 24
4x +5y +6z = 112
x +0y - z = 10

And we arranged the third order determinant as such that:
A = |1 1 1|
|4 5 6|
|1 0 -1|

Do you want to know what A comes up as?
It comes out as ZERO. (Call Lelouch, everyone!)

So it would pretty much be useless to compute for Ax, Ay and Az! Since the A is equal to 0! 8O

We all panicked. And people came in repeatedly announcing that if we can't find the answer in the choices, we should just write our own.
The problem?
As I just pointed out:
THERE IS NO FRIKKIN ANSWER.
D8 We all went into deep frustration over the fact that it was impossible to answer.

The frustration got worse to the point that I covered the page with scribbles, in my attempt to explain WHY IT WAS IMPOSSIBLE TO ANSWER. A doodle of a chibi-me saying that I can see the light (translation: I'm dying here!) with matching sparkles and everything. And every scribble of illegible numbers imaginable.

Until...

Isaac, all hail the mighty genius. Viva Isaac.

Yes Isaac.

He walked unto the platform, and said, "disregard her corrections. You'll get the answer. It's easy."

And I don't know with that arrogant, proud, selfish, grrrrrrrr person. But it hit me like an inspiration from out of nowhere.

And the page just got dirtier because I had to cross out every scribble I made on the margins and spaces of the page.
And I wrote my answer.

Although it was supposedly for the use of the Cramer's Rule, it was impossible to use. So I just used substitution and the common sense that every person has to have.

Let's just hope we're right.

For anyone who finds the answer, send me a note.