Thread: Basic linear

Hi!
I´m having some issues solving this equation system.






Nomatter what I do I cant eliminate the 2 terms to get one of the unknows alone. No problem eliminating 1 term thought if you ad the first 2 terms x_2 is eliminated... great and now lets eliminate one more term....emm emmm can´t do it! whats wrong...?
Any hints?
Thanks in advance

Originally Posted by Henryt999

Hi!
I´m having some issues solving this equation system.






Nomatter what I do I cant eliminate the 2 terms to get one of the unknows alone. No problem eliminating 1 term thought if you ad the first 2 terms x_2 is eliminated... great and now lets eliminate one more term....emm emmm can´t do it! whats wrong...?
Any hints?
Thanks in advance

There are infinitely many solutions to this set of equations, you cannot get simple numeric values for .

The way I would do this is let one of the variables, (I'll use ), and let this equal any constant , so we have

Now try and solve your equations in terms of lamba( ).

You already know that , your other 2 solutions will have the form where .

Hope this helps.

You can add the first two equations to get which is the same as . If you multiply the first equation by 3 and subtract the third equation from it you also get .

Since those are the same equation, you are right- you cannot continue and get a single equation in one variable. And, as craig says, that means there are an infinite number of solutions.

What you can do is this: solve for in terms of : . Now put that back into the first equation, so .

We can now write the solution set as . We can also write it as where I have taken to be the parameter t. The solution set is a plane which, because the set of equations is not homogeneous, does not contain the origin.