That's not a general solution. A general solution is a statement that lists each variable separately, along with its value (or expression). Halls already told you that z can be any Real number (therefore, the system has infinite solutions).
x = ?
y = ?
z = any Real number
Symbol z is the parameter (sometimes called a 'free variable' because it can take on any value). Symbols x and y will each be defined in terms of z.
To complete the general solution, solve your two equations above (the first one for x and the second one for y).
You may want to consider reviewing general solutions and parameterizations from intermediate algebra (i.e., from solving systems using the substitution or elimination method). That way, you'll understand what books or instructors are talking about, in these beginning topics of linear algebra.
I'm not sure what your source is for this exercise, but you can google to find
linear algebra videos for studying the topic from the beginning.
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