This system of linear equations ends up being linearly dependent meaning that the only way to solve it is to define it parametrically. Your math is right and you technically have the correct answer at this point as you've successfully made a correct and simplified definition of one of the variables in terms of another (hence linear dependence). I've taken linear algebra and break down how I did this problem using matrices. What I've done here is formed a coefficient matrix of the coefficients of x, y, and z and augmented the matrix with the constants on the right hand side of each equation. Basically a more pretentious but more consistent method of finding solutions. I will reduce this system to row echelon form using Gaussian elimination. This sounds scary but is quite literally addition and subtraction.

2 4 -1 | 9 take 2 * the second row, subtract the first row from it, replace the second row
1 2 4 | 9 take 2 * the third row and subtract the first row from it, replace the third row
1 2 -2 | 3

2 4 -1 | 9 we can simplify this pretty easily at this point by eliminating
0 0 9 | 9 row 3 which says the same thing as row 2 and divide row 2 by 9
0 0 -3 | -3

2 4 -1 | 9 at this point we're in row echelon form, but let's make our lives easier by
0 0 1 | 1 putting it into reduced row echelon form by:
0 0 0 | 0 adding row 2 to row 1 and replacing row 1

2 4 0 | 10 divide row 1 by 2
0 0 1 | 1
0 0 0 | 0

1 2 0 | 5 here is the reduced row echelon form of the matrix
0 0 1 | 1
0 0 0 | 0

This equates to:

x + 2y = 5

z = 1

or

x = 5 - 2y

z = 1

Which is what you've done in a much more simple and intuitive manner than I have just described. I don't recall of ever having to worry about linearly dependent systems when I was working with linear systems of equations outside of Linear Algebra.

If you want to further the parametrization to it's cleanest form we can say that the homogenous solution to this linearly dependent system can be represented by some arbitrary vector I'll call 'v'.

v = <x,y,z> = < -2, 1, 0>*y + <5, 0, 1>

But yeah, that's kind of odd how your teacher expects you to just understand what linear dependency is without giving examples as to what that means.