Solving a system of linear equations

[fluidistic]

Homework Statement

Find out if the following system of equation has solution. In case of having solutions, describe parametrically them all and give 2 of them explicitly.

2x-z=4
x-2y+2z=7
3x+2y=1


2. The attempt at a solution
I don't see nowhere in my notes what they want by "describe parametrically".
Anyway I've solved the system and it has only one solution : x=2, y=-5/2 and z=0.
As I just typed them, it is the explicit solution... I don't see how I could give 2 of them if there is only 1 solution. And much less parametrically.
Do you know what they mean?

 

[Mark44]

Homework Statement

Find out if the following system of equation has solution. In case of having solutions, describe parametrically them all and give 2 of them explicitly.

2x-z=4
x-2y+2z=7
3x+2y=1


2. The attempt at a solution
I don't see nowhere in my notes what they want by "describe parametrically".
Anyway I've solved the system and it has only one solution : x=2, y=-5/2 and z=0.
As I just typed them, it is the explicit solution... I don't see how I could give 2 of them if there is only 1 solution. And much less parametrically.
Do you know what they mean?

Your answer is the same as I got. I believe that the problem was asking was that if there were multiple solutions (which would then depend on one or two parameters), you should give two specific solutions. In this case, there is only one solution, and you have given it, so you're done.

 

[fluidistic]

Your answer is the same as I got. I believe that the problem was asking was that if there were multiple solutions (which would then depend on one or two parameters), you should give two specific solutions. In this case, there is only one solution, and you have given it, so you're done.

Ah ok! This is quite possible because there was more than one system of equations to solve.
Thank you.