Help with ordered triples

3x-2y-3z=4
x+3y-2z=5
6x-4y-6z=8

My friend is stuck on this problem and I can't seem to help her! All I can see is that equation 1 = (equation 3)/2

You have just found out the solution to the system of equations. If an equation is equivalent to another equation, any ordered triple of one equation is an ordered triple of the other equation. This means that there are infinite solutions.
Since there is still another equation (equation 2) that is not equivalent to the other equation, the ordered triples of the first and third equations also have to be ordered triples of the second equation.
Add the first and second equations.
4x + y - 5z = 9
Now, this equation has the same ordered triples of both the second and first (and hence third).
You can write out the solutions in set notation:
{(x, y, z) | 4x + y - 5z = 9}
This says that there infinite solutions, but the variables are still dependent on each other.

Your observation points out that there is no unique solution to the system since you don't have 3 independent equations. The first and third equations reduce to the same equation so the best you can do is solve for one of the unknowns in terms of the other two.

The solution is a 3-D line in space, the intersection of the two planes represented by the first two equations, not a unique point.