Question

If you were solving a system of equations and you came to a statement like 4 = 4, what do you know about the system?

Answer 1

the system is true

Answer 2

Is that true?
Does it depend on ANY variable?

Answer 3

idk

Answer 4

thats all it says

Answer 5

well if 4=4 then it is true

Answer 6

Hogwash. Please think more and type less.

Is 4 = 4 a true statement?

Answer 7

the system can't be solved

Answer 8

Does 4 = 4 depend on any value of x or y or z or t or s or q or p?

Answer 9

the system is already solved @Catch.me

Answer 10

lol

Answer 11

Is it 4x = 4y or just 4 = 4?

Answer 12

the values obtained satisfied both equations

Answer 13

idk its on one of my assignments. so I should say its true?

Answer 14

no 4 = 4 isn't a solution where x=5 or like that ? @Michiganboy21

Answer 15

You should answer my questions. This will lead you to the COMPLETE answer.

Answer 16

\[
\begin{array}{lcl}
x&=&x+1 \\
x\times 0&=&(x+1)\times 0\\
0&=&0\\
0+4&=&0+4\\
4&=&4
\end{array}
\]

Answer 17

I think what he mean is if we have like 2x+4y=8 and x+2y=4, then we would get 4=4 it cannot be solved.

Because you can factor 2 out from 2x+4y=8 and you will have x+2y=4, basically, you are given two same equations with two unknown variables, so it cannot be solved.

Answer 18

So @Catch.me is correct

Answer 19

@catch.me Your argument is incorrect. There are infinitely many solutions.

@JNoeller Your ONLY choices are 1) No solution or Cannot be Solved, 2) A single, unique solution, or 3) Infinitely many solutions.

Answer 20

Getting to \(4=4\) is easy.

Answer 21

@wio Really? I think we have to assume that it was worked CORRECTLY in order to obtain 4 = 4.

Answer 22

@JNoeller the question did not ask true or false. It ask what do you know about the system. It means there is a solution.

Answer 23

It cannot be solved because there is infinitely many possible value for variables, so there is no unique solution

Answer 24

Well then what should I say on the paper?

Answer 25

The THREE possible outcomes are categorized as follows:

1) Something ridiculous, like 3 = 7, THEN there is no solution and it cannot be solved.
2) Something conditional, like x = 4 and y = 5, THEN there is a unique solution and it is so solved.
3) Tautology, like 4 = 4, THEN there are infinitely many solutions, since this result does not depend on anything conditional.

Answer 26

yea you are right and for the same reason we don't divide by vector.@tkhunny

Answer 27

@geerky42 Your logic if flawed. Please read what you wrote.

1) It cannot be solved because
2) there is infinitely many possible value for variables,
3) so there is no unique solution

Rephrase
1) No solution
2) Infinitely many solutions
3) No unique solution.

Explanation:
1) Utterly disagrees with 2
2) This is correct.
3) Does not contradict #2

Answer 28

Repost of @geerky42
Because you can factor 2 out from 2x+4y=8 and you will have x+2y=4, basically, you are given two same equations with two unknown variables, so it cannot be solved.

this can be solved. it means that the values work in both equation and is an example of what i said, solution satisfies both equation

Answer 29

@JNoeller That was an awful lot of response in a very short time. Please read my posts carefully. These provide the complete solution and explanation. Hopefully, this will get everyone on the same page.

Answer 30

Given x + 4 = x + 4. What values for x satisfy this equation?
Subtract x from both sides, giving 4 = 4.
It is a tautology and there are infinitely many solutions.

Answer 31

There is difference between "no solution" and "cannot be solved"

Say you have equation y=x and you are asked to solve it. do that make sense? no because there is infinitely many possible values for x and y that satisfy this equation. how can you "solve" y=x ?

Answer 32

Example: 2x + 4y = 4 --- (1) and x + 2y = 2 ---- (2)
They both represent the same line as the second one is gotten by dividing the first one by 2. From (2): x = 2 - 2y. Put this in (1): 2(2-2y) + 4y = 4
4 - 4y + 4y = 4
4 = 4.

It means they are dependent equations. All points on the line are solutions. They have infinite number of solutions.

Answer 33

okay thanks tkhunny

Answer 34

Yes, it's infinite solutions, because it's coincidental lines. Hence the statement is true.

Answer 35

@geerky42 There is a bigger difference between "cannot be solved" and "infinitely many solutions". In the case of 4 = 4, "cannot be solved" is incorrect. It CAN be solved. There are infinitely many solutions.

x = y is easily solved. Pick any pair (x,y), such that x = y and you will have a solution. If you mean a UNIQUE solution, you must state that.

x = 2, y = 2 - Solved
x = 3, y = 3 - Solved

Unique solution? No.

Answer 36

alrights... you are right. excuse me for any inconveniences, I kind of have dyslexia

what I trying to say is that there is no unique solution...

Answer 37

Very good. I hope we're on the same page.

To explain a little more, give the result 4 = 4.

If we pick x = 7, is 4 = 4 still true? Yes. Then x = 7 is a solution.
If we pick x = 9, is 4 = 4 still true? Yes. Then x = 9 is a solution.
If we pick x = -17, is 4 = 4 still true? Yes. Then x = -17 is a solution.

The tautology 4 = 4 is independent of x (or any other variable expression). Pick anything you like and it will be a solution.

Answer 38

@preetha In 10 minutes, this generated 37 responses. I'd like to see another website do that!! :-)