# solve the following equation

• July 29th 2013, 08:27 AM
jakobjakob
solve the following equation
I have a hard time with the following equation, because it never checks out. If i only use 3 of the 5 equations in finding the solution the other 2 don't have the correct values for the soulutions to be right. I would really appreciate your help. Thank you very much for your time.

x + y + z = 2
2x - 3y - z = 5
x - 2y - 3z = -4
5x + y - 2z = -3
3x + 2y + 2z = 3
• July 29th 2013, 08:46 AM
ebaines
Re: solve the following equation
Why are there five equations? It takes three equations to allow you to solve for x, y and z. If you have more equations the additional ones are either (a) redundant or (b) inconsistent. Here if you solve for x, y, and z using the first three equations you get x= 1, y = -2 and z = 3. This solution also works for the 4th equation, but it doesn't work for the fifth - therefore the fifth equation is not consistent with the other four. Here's a simple example that may make it clearer - suppose you are give two equations with unknowns x and y:x+y = 2x = 1It's easy to see that y must equal 1. But suppose I throw in a third inconsistent equation:x+y=2x=1y=100Clearly it can't be that all three equations are true. This is what's happening with the 5 equations as you've written them. However, I wonder if there's a typo in your fifth equation? If it was 3x+3y+2z=3 then it would be consistent with the others (note the 3y term instead of 2y).
• July 29th 2013, 08:52 AM
jakobjakob
Re: solve the following equation
This question was on an exam for uni engineering so i think this is not likely to be a typo, probably just some trick that i'm not familiar with.
• July 29th 2013, 08:54 AM
ebaines
Re: solve the following equation
It must be either an error or there is no solution.
• July 29th 2013, 09:26 AM
Plato
Re: solve the following equation
Quote:

Originally Posted by jakobjakob
I have a hard time with the following equation, because it never checks out. If i only use 3 of the 5 equations in finding the solution the other 2 don't have the correct values for the soulutions to be right. I would really appreciate your help. Thank you very much for your time.
x + y + z = 2
2x - 3y - z = 5
x - 2y - 3z = -4

5x + y - 2z = -3
3x + 2y + 2z = 3

Quote:

Originally Posted by jakobjakob
This question was on an exam for uni engineering so i think this is not likely to be a typo, probably just some trick that i'm not familiar with.

Well there is your problem. Engineers are not mathematicians.

The first three equations have a common solution which is not a solution for the fifth equation.

Therefore, this is an inconsistent system of equations.
• July 29th 2013, 11:03 AM
jakobjakob
Re: solve the following equation
It was on some older exam of Math 2, subject at mechanical engineering uni course. I wasn't exactly clear before. That's why i have a hard time believing professor would give us the assignment worth 20% of final test to solve simple system of 5 equations with 3 unknown identities with an additional "typo".
@Plato: is inconsistent system of equations solvable or would the correct solution be : system is unsolvable?
• July 29th 2013, 11:12 AM
HallsofIvy
Re: solve the following equation
Yes, that is exactly what Plato said: "The first three equations have a common solution which is not a solution for the fifth equation." There is NO set of three numbers that satisfy all five equations. You ask in your last post "would the correct solution be : system is unsolvable?" Is that one of the options? You didn't say that initially.
• July 29th 2013, 11:13 AM
ebaines
Re: solve the following equation
There is no solution for three unknowns x, y and z that satsifies all 5 equations, and a university professor would certainly know that. So would any highschool math teacher. Again, I can't imagine why he would bother with more than three equations unless the correct answer to the question is: there is no solution. But to be completely sure - could you please post the question precisely as written on the exam?
• July 29th 2013, 11:45 AM
jakobjakob
Re: solve the following equation
@ebaines: Here is the exact copy of exam, excercise 3:
http://valjhun.fmf.uni-lj.si/~mihael...iti/080612.pdf
Rough translation of instructions for the excercise: Find all solutions of system of equation.
• July 29th 2013, 03:12 PM
Plato
Re: solve the following equation
Quote:

Originally Posted by jakobjakob
@ebaines: Here is the exact copy of exam, excercise 3:
http://valjhun.fmf.uni-lj.si/~mihael...iti/080612.pdf
Rough translation of instructions for the excercise: Find all solutions of system of equation.

dnm you are hardheaded are you not?

Have a look at this webpage.

That set of calculations tells us that $x=1,~y=-2,~\&~,z=3$ is a unique solution set for the first three equations.
You can see that the set does not solve the fourth nor the fifth equation.

You can change the input vectors on that webpage to solve any of the other three equations.
• July 30th 2013, 04:59 AM
ebaines
Re: solve the following equation
The reason I asked for the exact wording is that often posters use short cuts in terminology or misinterpret how the question is worded. In this case the OP has faithfully written the problem exactly as the exam had it. What's really strange is that the solution for the first three equations actually works for the fourth (though not the fifth). I can't fathom what the professor was thinking, unless he is expecting the answer "there is no solution."