Question

Find the solution set of the following equations:
X-2y+3z = 5

Answer 1

,,equations" - where are ?

Answer 2

It looks like there's only 1 equation, and 3 variables.

x = 2y - 3z + 5
y = y
z = z
\[\left[\begin{matrix}x \\ y \\ z\end{matrix}\right] = \left[\begin{matrix}2r -3s + 5\\ r \\ s\end{matrix}\right] = r\left[\begin{matrix}2\\ 1 \\0 \end{matrix}\right] + s \left[\begin{matrix}-3\\ 0 \\ 1\end{matrix}\right] + \left[\begin{matrix}5 \\ 0 \\ 0\end{matrix}\right]\]

r and s can be anything.
Are you sure your question is right though? xd

Answer 3

This equation represents a plane, you can represent the solutions with the parametric form

Answer 4

Yup, there’s only one equation with three variables.

Answer 5

Let me post the actual picture of the question for you guys lol

Answer 6

if it's just 1 equation, then you have your answer right up there.

Answer 7

The answer is written in some other way... let me post ..one sec

Answer 8

Wait, let me show you a method that I’ve been using to solve these questions... one second plz

Answer 9

So their k1 and k2 is just like my r and s.

But I think they did
z = (5/3) + (2/3)y - (1/3)x

Answer 10

So this is the template I’ve been using to solve these kinda questions

Answer 11

Yeah that works

Answer 12

But please tell me why did they divide both sides by 3 instead of 2 or 1??

Answer 13

Do you want me to draw for you sir? :)

Answer 14

because they were solving for z

Answer 15

Why z in particular?

Answer 16

it doesn't have to be z, it can be x or y actually.

Answer 17

So does that mean if you divide and isolate for let’s say y variable, we should come to the same answer in the end?

Answer 18

So my solution was
\[\left[\begin{matrix}x \\ y \\ z\end{matrix}\right] = \left[\begin{matrix}2r -3s + 5\\ r \\ s\end{matrix}\right] \]
and their solution was
\[\left[\begin{matrix}x \\ y \\ z\end{matrix}\right] = \left[\begin{matrix}r\\ s \\ \frac{5}{3}-\frac{1}{3}r+\frac{2}{3}s\end{matrix}\right] \]


hmmm

Answer 19

I never explored this, but theoretically...the should have the same "Solution space"

There's infinite number of solutions, but not every number is a solution, so we call it a solution space.

Answer 20

Is there a video on this topic ?

Answer 21

My textbook literally didn’t do any sample questions for this particular topic

Answer 22

3blue1brown might have a good video on this

Answer 23

Thanks bro, really appreciated:)