
infinite solutions
Hello, we have been solving linear equations in three variables and one of them has the final two equations as:
x3z=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.

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?)

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, x3z=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