If the solution to a three variable system of linear equations is x+y=3 and z=1, is this a dependent linear system?

Question

I got the answer x+y=3 and z+1 for a system of three linear equations with three variables but I don't know if it is defined as a dependent linear system or not.  It is multiple choice answers : a) no solution b)infinite solutions c) inconsistent d) a dependent linear system e) none of the above.

 

the equations are:

x+y+z=4

x+y+2z=5

4x+4y+6z=18

Answer 1

There are infinite solutions for x and y but z=1 consistently. There is linear dependence between x and y. z is independent of x and y.

Comments

Come on Rod! That was not fair! You deleted my answer and then.....you just made me cry. :(

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I'm so, so sorry, little buddy. That was not my intention, to make you cry. I know you try very hard, but to answer a question like this is not something you've learned to do yet. And that's OK. To answer a question honestly with understanding is what it's all about, so that you can truly help the person asking the question. They may be as desperate to know the answer to their questions as you are to know the answer to your questions. Anyway, I'll be more careful not to upset you again. If it helps, I did think a lot about whether I should hide your answer, because I could see you had tried; but I also had to think about the person asking the question and whether your answer would help or confuse them.