infinite solutions

• Mar 13th 2011, 11:37 PM
fran1942
infinite solutions
Hello, we have been solving linear equations in three variables and one of them has the final two equations as:

-x-3z=-1
x+3z=1

which will answer as an infinite number of solutions possible.

My question is, is it acceptable to simply write "infinite number of solutions possible" in an exam, or should I express that some other way ?

Thanks for any help.
• Mar 13th 2011, 11:42 PM
Prove It
Yes. You can add that this is because the two equations are identical (what happens when you multiply both sides of the first equation by -1?)
• Mar 14th 2011, 05:57 AM
HallsofIvy
If you wanted to really impress (and/or shock) your teacher, you could find a general expression for all of those "infinite" number of solutions. Of course, that would depend upon what the first equation was.

If the problem was, say, x+ y+ z= 1, -x-3z=-1, x+3z=1, you could rewrite the last equation as x= 1- 3z and put that into the first equation to get 1- 3z+ y+ z= 1+ y- 2z= 1 so that y= 2z. Now you can write that (x, y, z)= (1- 3z, 2z, z) is a solution for z any number