# Thread: unique solutions to system of equations.

1. ## unique solutions to system of equations.

I was under the impression that a system has a unique solution if its determinant was not equal to zero. This website seems to verify this fact https://math.oregonstate.edu/home/pr...em/system.html
Below are the solutions my teacher has provided to the question. But who is right? Do you get a unique solution if you set the matrix equal to zero or do you get a unique solution if you set the matrix not equal to zero?

2. ## Re: unique solutions to system of equations.

I agree with you. A linear system has a unique solution if the corresponding system-matrix has a non-zero determinant. I think your teacher implicitly means that the solution is given as the set:

$\displaystyle \mathbb{R} \setminus \lbrace -1 , -3 \rbrace$

3. ## Re: unique solutions to system of equations.

Your teacher explicitly states the values of $k$ that you left implicit. But you never actually said in your answer what you think those values represent.

It's not sufficient in solving a problem, to just scribble some lines. You should explain what you are doing and why, and clearly state your final result.

Why did you transform the matrix like the anyway?

4. ## Re: unique solutions to system of equations.

This is not my work. This is my teachers solution to the question... I am just trying to understand it.

Krisly, what does your notation mean in English?

5. ## Re: unique solutions to system of equations.

It means, the real numbers without the set consisting of $\displaystyle -1$ and $\displaystyle -3$. It is equivalent to say $\displaystyle k$ can be anything except $\displaystyle -1$ or $\displaystyle -3$.