!!

[tulip moat]

:)

[vague thorn]

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[tulip moat]

@tacit orchid

[tacit orchid]

okay well what is your first thought

[tulip moat]

X + Y + Z = 25
4x - 2y - z = 55

4 if he got it right, -2 if he got it wrong, and - 1 if he didn't answer any questions

[tulip moat]

X = 25 - Y - Z?

I'm not sure on what to do next

[tulip moat]

@plain monolith

I'm very sorry for shark, but i need to finish this question tonight

[plain monolith]

Solve the system generally. I assume the rest can be checked with brute force.

[tulip moat]

I dont think i quite understand how it works

[plain monolith]

Solve the system using Gauss's method first.

[tulip moat]

1 + 1 + 1 = 25
4 + -2 - 1 = 55 (?)

I just searched google

[plain monolith]

Uh...

Can you solve the system or not?

[tulip moat]

I dont think so

[plain monolith]

We have:
x + y + z = 25
4x - 2y - z = 55
Start by writing the matrix of this system.

[tulip moat]

Actually, do you mind explaining the Gauss method, if it's too long then it's fine

[plain monolith]

Oh.

I assume you haven't studied linear algebra.

Then just solve the system using an approach you know. Substitution, for example.

[tulip moat]

4(25 - y - z) - 2y - z = 55

[tulip moat]

I did but only the simple ones

[tulip moat]

I dont understand how to find y tho through this

[plain monolith]

Simplify it, then express y in terms of z.

[tulip moat]

8x - 6y - 5z = 55

I forgot how to do the next step

[plain monolith]

Wait, where did x come from?

[plain monolith]

You only have y and z here.

[tulip moat]

Wait, um 100 - 6y - 5z = 55

I guess

[plain monolith]

Right. So, now you can express y in terms of z.

[tulip moat]

can you help me with this one

[plain monolith]

You have a linear equation in y and z. Express y in terms of z.

[tulip moat]

[tulip moat]

-6y = 5z + 45 (?)

[plain monolith]

Well, -6y = 5z - 45, rather. So, what is y?

[tulip moat]

There's more to count?

[plain monolith]

Well, you have expressed -6y. We need to express just y.

[tulip moat]

Y= 5z - 45/6

?

i promise I'm trying

[plain monolith]

No.

[tulip moat]

are you free at the moment?

is it possible if we could get in a call, and you draw me some explanation?

[plain monolith]

Sorry, can't join a call right now.
I suggest you review the topic of solving linear systems.

[tulip moat]

Ah i see, no worries

[tulip moat]

Then, what's the right answer?

[plain monolith]

Well, I won't just tell the answer.

As I said, review the topic first, then you can solve this problem.

[tulip moat]

but it's 23:28

[tulip moat]

Am i almost finished with the questions, if i learned linear systems and got that part right, am i close to finishing the question?

[plain monolith]

Yes. You express x and y in terms of z, then just try various values of z, noting that they must be integers between 0 and 25.

[tulip moat]

STAY ONLINE OKAY

IM FINISHING THIS QUESTION

[plain monolith]

Well, ok...

[tulip moat]

This makes no sense

[tulip moat]

Y = 7.5 - 5z

YES?

[plain monolith]

No.

Just divide both sides by -6.

[tulip moat]

6y/6 = - 5z + 45/ 6

Is this what you mean

Is it

Y = - 5(2 + 9)/6

[tulip moat]

Is it correct this way?

[plain monolith]

No.

Let me show this step, I guess...

[tulip moat]

yes please

when I'm done with this question, I'm going to flex to everyone

[plain monolith]

We have the system:
x + y + z = 25
4x - 2y - z = 55
We express x from the first equation.
x = 25 - y - z
Then we substitute it into the first and simplify.
4(25 - y - z) - 2y - z = 55
100 - 4y - 4z - 2y - z = 55
6y + 5z = 45
Now we express y.
6y = 45 - 5z
y = 15/2 - (5/6)z

[plain monolith]

No offense, but this is a very easy question.

[tulip moat]

okay

[plain monolith]

So, we have y in terms of z. Now, substitute that into one of the initial equations (first one would probably be easier). Then express x in terms of z.

[tulip moat]

I dont understand how you get 15/2 - (5/6)z

[plain monolith]

I divided both parts of 6y = 45 - 5z by 6.

[tulip moat]

Like 45 ÷ 6?

[plain monolith]

Well, that and also -5/6.

[tulip moat]

Okay i get it

but how 15/2

in what way

like i know it both has a total of 7.5, but like how you think of putting 15/2

[plain monolith]

Because 45/6 = 15/2.

[tulip moat]

Okay

I think it's just the tiredness my bad

[plain monolith]

You should review the topic and solve this problem later.

[tulip moat]

It's okay, we're almost done

X = 35/2 - 1/6 z

[tulip moat]

right

there's no way it's wrong

[plain monolith]

Nice! So, we have:
x = 35/2 - (1/6)z
y = 15/2 - (5/6)z
Now, recall that x, y, z are all integers between 0 and 25. So, what values of z do we need to check?

[tulip moat]

OAHAISHHAAH YEYEYEYYEYE

Uh

man

[plain monolith]

What?

[tulip moat]

6

I think

[plain monolith]

No. And we need to check several values of z.

Again, remember that x, y and z must be integers.

[tulip moat]

was it a close guess

[plain monolith]

Look at the first equation, for example. What form must z have so that x is an integer?

Better to start by thinking about what form (1/6)z must have.

[tulip moat]

5?

[plain monolith]

No.

We must have integer x.

Is 35/2 an integer?

[tulip moat]

Yes?

[plain monolith]

Um...

[tulip moat]

No

It's nkt

[plain monolith]

Yeah, it isn't. It is, however, a half-integer.

So, if we want to add (or subtract) another thing to it, it must also be a half-integer.

So, (1/6)z has the form n + 1/2, where n is an integer. What form does z have, then?

[tulip moat]

I dont know

[plain monolith]

Well, if (1/6)z = n + 1/2, what is z?

[tulip moat]

I dont know simple math

[plain monolith]

That's why I recommend reviewing this topic first.

We may be able to finish this problem eventually, but it doesn't matter if you don't understand how to solve it.

[tulip moat]

I'll learn the topic more after this question

See it as if I'm trying to solve the exercise question

[tulip moat]

Z = 6( n + 1/2) ?

[plain monolith]

Yes. So, z = 6n + 3.

So, just check numbers of that form from 0 to 25.

[tulip moat]

Okay

0, 6, 12, 24 are possible

[plain monolith]

No. Those are the numbers of the form 6n. You need 6n + 3.

[tulip moat]

Oh

3, 9, 15, 21

[plain monolith]

Right. So, now check for which value of z we get integer values of both x and y.

[tulip moat]

3

[plain monolith]

Well, 3 works. Anything else? Make sure to write the values of all the three variables: x, y, z.

So, for z = 3 we get (x, y, z) = (17, 5, 3).

[tulip moat]

z = 3 (x, y, z) = (17, 5, 3)
z = 9 (x , y, z) = (16, 0, 9)
z = 15 (x , y, z) = (15, -5, 15)
z = 21 (x , y, z) = (14, -10, 21)

[plain monolith]

Well, as x, y, z must be between 0 and 25, the latter two don't count.

So, just (17, 5, 3) and (16, 0, 9).

Now, read the statement of the problem again.

[tulip moat]

okay

James got 17 questions right ?

Thank you so much for teaching me, even though i was a little hard headed for not learning the topics beforehand but i really appreciate your thoughts and efforts.

[plain monolith]

Well, notice that James didn't think he attempted a lot of questions.
(17, 5, 3) corresponds to him attempting 22 questions, while (16, 0, 9) corresponds to 16 attempted questions. So, I'd say the latter works better.

Ah, wait.